Properties of cube numbers

Let’s look at the cube of numbers from 1 to 50

Let’s see some pattern in it, and find properties of cube numbers

Number of zeroes at the end of a perfect cube is always multiple of 3

So, number of zeroes at the end can be 3, 6, 9, 12, 15,....

Example

• 1,000 is a perfect cube
• 8,000 is a perfect cube
• 27,000,000 is a perfect cube
• 64,000,000,000 is a perfect cube
• 20 is not a perfect cube
• 400 is not a perfect cube
• 80,000 is not a perfect cube

Cube of even numbers are always even,

Cube of odd numbers are always odd

Example :

Cube of 2 is 8,

Cube of 6 is 216

And

Cube of 7 is 343

Cube of 9 is 729

Unit digit of cube of any number will be the unit digit of the cube of its last digit

Check Explanation 

The cube of a negative integer is always negative

Example 

(-1) ³ = (-1) × (-1) × (-1) = -1

(-2) ³ = (-2) × (-2) × (-2) = -8

The sum of the cubes of first in  natural numbers is equal to the square of their sum

1 ³ + 2 ³ + 3 ² +..........+ n ³ = (1 + 2 + 3 +..........+ n) ²

Example 

1 ³ + 2 ² + 3 ³ + 4 ³ = (1 + 2 + 3 + 4) ²

1 + 8 + 27 + 64 = (10) ²

100 = 100

Cubes of the number ending in digit 1, 4, 5, 6 and 9 are the numbers ending in the same digit