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# What is cubed in math? Cubed Number: The final answer received by multiplying a whole number by itself three times is called cubed number or cube number.

For example: 11 x 11 x 11 = 1331

1331 is called the cube of 11.

### Representation

There are two ways to represent a cube number. Let’s check.

Way 1:  Expanded Form

Here you write the number in the multiplication form. Let’s check few examples

a  x a x a

7 x 7 x 7

Way 2: Superscript Form

For a cube number, represent the number with 3 as superscript. Here are a few examples

a

73

## How to cube a number?

To find cube of a number

Step 1: First multiply it by itself. This is also known as square of a number.

Step 2:  Now again multiply the same number with the result obtained in Step1.

So as per these steps, let’s find the cube of 27.

Step 1: 27 x 27 = 729

Step 2: 729 x 27 = 19638

So, the cube of 27 is 19638. This can also be written as

27= 27 x 27 x 27 = 19638

Let’s take another example

22= 22 x 22 x 22 which turns out to be 10648

Have a look at cubes of first 10 natural numbers

13 = 1 x 1 x 1 = 1

23 = 2 x 2 x 2 = 8

33 = 3 x 3 x 3 = 27

43 = 4 x 4 x 4 = 64

53 = 5 x 5 x 5 = 125

63 = 6 x 6 x 6 = 216

73 = 7 x 7 x 7 = 343

83 = 8 x 8 x 8 = 512

93 = 9 x 9 x 9 = 729
103 = 10 x 10 x 10 = 1000

## What is a perfect cube?

If a number can be broken into a product of three same numbers, it is called a perfect cube.

### Find if a number is a perfect cube or not

Perform prime factorization of the number. If the factors can be grouped into three exact sets of similar numbers, only then it’s a perfect cube.

For example:

• 1700 = 17 x 10 x 10

1700 is not a perfect cube as it has only two 10’s and one 17.

• 1728 = 12 x 12 x 12

1728 is a perfect cube as it is made by multiplying 12 three times.

Properties of cube numbers

1. When an even number is cubed, the answer is also even. For example: 14 x 14 x 14 = 2774. 14 and 2774 both are even numbers.
2. When an odd number is cubed, the result is also odd. For example: 13 x 13 x 13 =2197. Here, 13 and 2197 both are odd numbers.
3. The cubes of numbers ending in 1,4, 5, 6 and 9 also have the same number at the unit’s place. For example: In, 14 x 14 x 14 = 2774, 14 and 2774 both end in 4.
4. If we add the cubes of first n natural numbers, the answer is equal to all the numbers added together and then squared.

13 + 2 3 + 33 + … + n3 is equal to (1 + 2 + 3 + … + n)2

Example:  Let’s add cubes of first 5 natural numbers
13 + 2 3 + 33 + 43+ 53

= 1 + 8+ 27 + 64 + 125

= 225

This is same as (1 + 2 + 3 + 4 + 5)2 = (15) 2 = 225 ##### Unleash the Power of visualization to break tough concepts

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