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

Number Cube
1 1
2 8
3 27
4 64
5 125
6 216
7 343
8 512
9 729
10 1000
11 1331
12 1728
13 2197
14 2744
15 3375
16 4096
17 4913
18 5832
19 6859
20 8000
21 9261
22 10648
23 12167
24 13824
25 15625
30 27000
35 42875
40 64000
45 91125
50 125000

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

Number Cube
1 1
2 8
3 27
4 64
5 125
6 216
7 343
8 512
9 729
10 1000

 

 

 

  1. Chapter 7 Class 8 Cubes and Cube Roots
  2. Concept wise

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.