Shortcut to find the Cube of a number

Very often we have to find the cube, i.e. third power of 2 digit numbers. Cubes of very large numbers are rarely used.

Cubes of all the single digits should be memorized. Find below the table of cubes of first ten natural numbers –

13 = 1,              23 = 8,              33 = 27,            43 = 64,            53 = 125,

63 = 216,          73 = 343,          83 = 512,          93 = 729,          103 = 1000

To find the cube of any 2 digit number, we have to take the following steps

First Step: The first thing we have to do is to put down the cube of the tens-digit in a row of 4 figures. The other three numbers in the row of answer should be written in a geometrical ratio in the exact proportion which is there between the digits of the given number.

Second Step: The second step is to put down, under the second and third numbers, just two times of second and third number. Then add up the two rows.

Finding the cube of 12

Or, 123 = ?

First Step: Digit in ten’s place is 1, so we write the cube of 1. And also as the ratio between 1 and 2 is 1:2, the next digits will be double the previous one. So, the first row is

1 2 4 8

Step II: In the above row our 2nd and 3rd digits (from right) are 4 and 2 respectively. So, we write down 8 and 4 below 4 and 2 respectively. Then add up the two rows. Ex 2: 163 = ?

Soln: Explanations: 13 (from 16) = 1. So, 1 is our first digit in the first row. Digits of 16 are in the ratio 1:6, hence our other digits should be 1×6 = 6, 6×6 = 36, 36×6 = 216. In the second row, double the 2nd and 3rd number is written. In the third row, we have to write down only one digit below each column (except under the last column which may have more than one digit). So, after putting down the unit-digit, we carry over the rest to add up with the left-hand column. Here,

i) Write down 6 of 216 and carry over 21.

ii) 36 + 72 + 21 (carried) = 129, write down 9 and carry over 12.

iii) 6 + 12 + 12 (carried) = 30, write down 0 and carry over 3.

iv) 1 + 3 (carried) = 4, write down 4. Vineet Patawari

Hi, I'm Vineet Patawari. I fell in love with numbers after being scared of them for quite some time. Now, I'm here to make you feel comfortable with numbers and help you get rid of Math Phobia!

111 thoughts to “Shortcut to find the Cube of a number”

1. Jeeva says:

how to find cube of 23?

1. Akash Asija says:

Ratio is 2:3
Cube of Tens Digit is 8, i.e. cube of 2
Now other four digits in geometric progression exactly as the ratio of question digits are
8:12:18:27
Now, twice of 2nd and 3rd number just below the respective numbers
8:12:18:27
+ :24:36:
8:36:54:27
Now, let the no. 7 in own place and Carry over 2 to left it will become 56
Now, let the no. 6 in own place and carry over 5 to the left it will become 41
Now, let the no. 1 in own place and carry over 4 to the left it will become 12

12167

1. Arpitkumar Yadav says:

I tried cube of 49 by this method it is coming out to be something different. Try it

2. EXCELLENT CAREER POINT says:

1. BASIC CONCENTRATION
3. DMIT
4. SUPER MATHS
5. SUPER MEMORY

3. roshan biswal says:

the cube of 23 is 12167.

4. BISWAJIT says:

I want to find out the cube of 0. 333333345
How can I get this . pl tell me.

5. Sachin Jaiswal says:

It is very helpful to find cube. Thanks…

1. Anshul Jaiswal says:

I am lavish do you know me of Satna if yes then reply

6. mayaank says:

Helo

7. Manjesh Lodhi says:

Its a good trick to find cube in less time

8. sabina says:

cube of three digit number????

9. haribansh says:

i think it will be better to find the square and then multiply it using shortcut method.

1. admin says:

That’s the beauty of calculations. You can always do it your way. One should explore various ways doing calculations but adopt the one where he is most comfortable.

Thanks

1. sabina says:

how to calculate the cube of three digit number?

2. sabina says:

can u plz tell me how to calculate cube of three digit number?

3. KriSHA says:

Sir can we find cubes of some other nos through this method like
53 ,99 ,115

4. shalki says:

great and nice trick !

10. Mani says:

Plese tell the method to find::

The least number to be added with 1720 to make it as a perfect cube??

11. TO FIND THE SQUARE OF A NO. WHOSE UNIT PLACE IS 5
EG:-if wehave 2 find the square of 15 then multiply first 5*5 then multiply 1 with
more than 1 i.e 1*2=2 & wite 2 before 25 i.e 225

1. roshan says:

hi a am also Roshan.

12. Hannah Aguaras says:

THANK YOU SO MUCH!!!!!!!!

13. Asif says:

what is the method to find cube of 88,222,6666,…. etc. ?

14. Asif says:

what is the method to find cube of 222, 88, 6666…etc?

1. Akash Asija says:

Ratio is 8:8
Cube of Tens Digit is 512, i.e. cube of 8
Now other four digits in geometric progression exactly as the ratio of question digits are
512:512:512:512
Now, twice of 2nd and 3rd number just below the respective numbers
512: 512 : 512 :512
+ : 1024: 1024:
512:1536 :1536 :512
Now, let the no. 2 in own place and Carry over 51 to left it will become 1587
Now, let the no. 7 in own place and carry over 158 to the left it will become 1694
Now, let the no. 4 in own place and carry over 169 to the left it will become 681

681472

15. mani says:

how to find out cube of any number Ex:25,56,86 etc based on your find a cube of any number? i tried your method but i am not getting write answer.

1. noops says:

how to find out cube of any number Ex:25,56,86 etc based on your find a cube of any number? i tried your method but i am not getting write answer.

2. Sumit Kumar says:

It means that you are making mistakes in calculating. Here is the solution for
25.
Cube of 2, the first letter in the number is 8. Now put the next 3 numbers using the 2:5, that is,
8 20 50 125
40 100
__________ Now start from the left.
8 60 150 125
8+60+(150+12)\5 = 8+60+162\5 = 8+(60+16)\25
8+76\25
(8+7)/625
15625

3. Jugal says:

STEP 1. TAKE ANY NUMBER U WANT TO FIND THE CUBE.

STEP 2. WRITE THE CUBE OF THE DIGIT PLACE NUMBER..

for eg: if 56 is the number… write the cube of 6.. ie 216

STEP 3. WHATEVER ANS U GET WRITE ITS LAST DIGIT N CARRY THE REMNG NUMBERS..

for eg: in above eg write 6 and carry 21

STEP 4. THEN MULTIPLY BOTH THE DIGITS OF THE NUMBER U SELECTED TO FIND THE CUBE.AND AGAIN MULTIPLY THAT ANS BY 3.

for eg: if u select 56… then multiply 5 and 6 ie 30 and multiply 30 by 3.. ie 90

STEP 5: MULTIPLY THE ANS U GOT BY THE NUMBER U SELECTED TO FIND THE CUBE…

for eg: ie in above eg multiply 90 by 56 ie = 5040

STEP 6. NOW, CONSIDER ONLY THE LAST TWO DIGITS AND CARRY THE REMAINING OF THE ANS U GOT AND ADD THE LAST TWO DIGITS BY CARRY NUMBER IN STEP 3

for eg: the carry number was 21 and the last two digit of ans is 40.. so add 40 and 21 ie=61

STEP 7. NOW WRITE THAT NO. ON THE LEFT OF ANS U GOT IN STEP 2.

for eg… cube of 6 216… u wrote 6 and carried 21.. by following step 5 and 6.. u got 41,,, so write it as … 416

STEP 8: NOW FIND THE CUBE OF REMAINING DIGITS OF THE NUMBER U SELECTED AND ADD IT BY THE CARRY IN STEP 6.. AND WRITE THE ANS BESIDE STEP 7

for eg: cube of number 5 in 56 is 125… add it by 50 (carry in step 6).. ie 125+50=175.. now write 175 beside 416… ie 175416

STEP 9: THE CUBE OF UR NUMBER IS READY 🙂

TRY IT IT IS MY INVENTION

JUGAL

16. jeevan says:

short trick 1-30 cube

17. SanthoshKumar Potnuru says:

For eg:57
5^3=125, 7^3=343
5/7(343)=245
5/7(245)=175 350=175*2,,,,,490=245*2
125 175 245 343
350 490
____________________
185193

1. Sneha says:

will u plz explain the last line ….how it will calculate

18. ABHI says:

one of the best websites for the pupil who attends competitive exams

19. Kavita Anuragi says:

How to calculate cube of 57, 83???

1. ubisch says:

take ur calculator and find the answer

2. VINAY says:

(57) KA CUBE = 5*5*5 5*5*7 5*7*7 7*7*7
125 175 245 343
350 490
_______________________________________
Now Simply Carry forward & add from R to L =185193
_______________________________________
This is how U can Solve d Cube Of any two digit Number .

1. Guest says:

Hello!!Mr. vinay, do u call this a shortcut?!

2. ashish says:

how u get 350 and 490

3. ashish says:

350 and 490 should be under 175 and 245 respectively,,,

4. deepak says:

how do u get the 350 and 490 can u explain

5. inder says:

osm way.

20. ahmed says:

This is a written method of calculating cubes of numbers by paper & pencil.

What is the quick, MENTAL, method ?

1. Prem kumar says:

First u should know how it is calculated then try to calculate without pen and paper. https://youtu.be/0gDr09J7WHw

21. simple says:

Nice way to calculate Cube ..how can we calculate cube of 23.

22. simple says:

Ho w to calculate cube of 23 ??

1. roshan biswal says:

the cube of 23 is 12167.

23. ahmed says:

This ” Vedic” method is OK if one has to *calculate* the cubes of numbers in writing.

Do you have a method of getting these answers, totally by mental calculation, from inside ones head ??

24. shubham says:

very nice and quicker way to do mathematics