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.

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.

a³ 3a²b 3ab² b³

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.

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

(a+b+c)^3 …. multiply it out 🙂

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

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

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

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.

nice

its very helpful

19 cube

ratio of digits: 1 : 9

continue the ratio as 1: 9: 81 :729

double the middle two ratios: 18 162

add them using usual additions

and carry the 10th, 100th etc to

the next number and complete

the addition. 5 31 72

1 : 9 : 81 : 729

18 162

————————

6 8 5 9

Therefore cube of 19 is 6859

sir if you dont mind can you explain it in more lucid manner.

I am unable to understood after doubling the ratios.

Sir please help me