# Shortcut to find cube of any number from 1 to 100

Finding cube of a number above 20 in the usual way is difficult and time consuming. With this Shortcut to find cube of any number, you can easily calculate cube of a number within seconds.

## Short cut to find cube of number steps

Step 1: Assume the ten’s place number of the given number as a and the unit’s place number as b.
Step 2: Now, we all know that (a+b)³=a³ + 3a²b + 3ab² + b³

We shall manipulate the same formula to calculate the cube of a number.

(i)Find b³ to get the last digit
If you get two digit number then, add ten’s place digit to 3ab²
(ii) Find 3ab²
If you get two digit number then, keep the unit’s place digit and and
add ten’s place digit to 3a²b.

(iii) Find 3a²b
If you get two digit number then, keep the unit’s place digit and and
add ten’s place digit to a³.

(iv) Find a³
If you get two digit number then, just add the carried forward digit if any
and write the number.
Cube of any 2 digit number will be in the pattern of
a³ 3a²b  3ab² b³

Cube To make things easier it is good to memorize the cubes of numbers from
1 to 10
13=1
23=8
33=27
43=64
53=125
63=216
73=343
83=512
93=729

## Examples

Lets use this method to calculate the cube of a number with help of an example to understand better

Example 1: 32³=?
Step 1: Assume a= 3 and b= 2
Step 2: Now substituting the values of a and b in the below pattern
a³ 3a²b  3ab² b³

(i) Finding b³  Now that is
b³=2³=8
We get the last digit as 8.

(ii) Finding 3ab²
3ab²=3(3)(2)²=36
From this we will keep the one’s place digit(6) and add the ten’s place digit(3) to 3a²b.

(iii)Finding 3a²b and adding ten’s place digit(3)
3a²b=3(3)²(2)=3(9)(2)=54 + 3= 57

From this we will keep the one’s place digit(7) and add ten’s place digit(5) to b in the next step.

(iv) Finding a³ and adding the ten’s place digit(5) from previous step
a³=3³=27+5=32
From this we get the number as 32

From all the above steps we get

Ans 32³=32768

Example 2: 47³=?
Step 1: Assume a= 4 and b= 7
Step 2: Now substituting the values of a and b in the below pattern
a³ 3a²b  3ab² b³

(i) Finding b³  Now that is
b³=73=343
We get the last digit as 3.

(ii) Finding 3ab²
3ab²=3(4)(7)²=12 x 49=588 (Tip: Use Shortcut to multiply any 2 digit by 2 digit)
Now add 34 that you got from step 1 to 588,we get  588+34=622
From this we will keep the one’s place digit(2) and add remaining digits(62) to 3ab².

(iii)Finding 3a²b and adding remaining digits of step 2(62)
3a²b=3(4)²(7)=16 x 21=336
336+ 62=398
From this we will keep the one’s place digit(8) and add remaining digits(39) to a³.

(iv) Finding a³ and adding the remaining digits from step 3
a³=4³=64
64 + 39=103

From all the above steps we get
47³=103823

With practice you will be able to find the cube of any two digit
number within seconds.

Try it  with other numbers and let us know if it was helpful to you!

If you have any other shortcut way of finding the cube of a number,
feel free to share it here.

### 0 thoughts on “Shortcut to find cube of any number from 1 to 100”

1. what about 3 digit number. say for example. 110, 106, 120 etc..?

2. (a+b+c)^3 …. multiply it out 🙂

3. this trick will not work for number 45

• It works for 45^3 too. It is as under.
45^3= 4^3+3(4)(4)(5)+3(4)(5)(5)+5^3
=64+240+300+125=64+240+312+5=64+271+2+5=91+1+2+5
=91125

4. i think this is the easiest trick i got to know thaxx a lot……….

5. this trick is not working for numbers that ends with 7 it gives one number less in the middle than the actual answer for eg.47^3=103823 and the ans this trick gives is 103723 same with the case of 57^3=185193 and it gives 185093 i tried it with all the nos. and it failed…

• It works for both cube of 47 , 57 . You did mistake i think

6. You can use the same trick to find 47^3 and 45^3 .It works.
We have worked that for you.
You can refer the steps and check for some more numbers.

7. nice

8. 19 cube
ratio of digits: 1 : 9
continue the ratio as 1: 9: 81 :729
double the middle two ratios: 18 162
and carry the 10th, 100th etc to
the next number and complete
1 : 9 : 81 : 729
18 162
————————
6 8 5 9
Therefore cube of 19 is 6859

• 