If you multiply a number by itself and then by itself again (thrice), the product is a cube number. It is also called as a perfect cube. That is, if \(a\) is a number, its cube is represented by \(a^3\).
Example:
Let us find the cube number of \(3\).
Here, \(a = 3\).
\(a^3 = 3^3\)
\(= 3 \times 3 \times 3 = 27\)
Therefore, \(27\) is the cube number of \(3\).
The following table consist of cube numbers of the first ten numbers.
|
Number
|
Cube number
|
Number
|
Cube number
|
|
1
|
\(1^3 = 1\)
|
11
|
\(11^3 = 1331\)
|
|
2
|
\(2^3 = 8\)
|
12
|
\(12^3 = 1728\)
|
|
3
|
\(3^3 = 27\)
|
13
|
\(13^3 = 2197\)
|
|
4
|
\(4^3 = 64\)
|
14
|
\(14^3 = 2744\)
|
|
5
|
\(5^3 = 125\)
|
15
|
\(15^3 = 3375\)
|
|
6
|
\(6^3 = 216\)
|
16
|
\(16^3 = 4096\)
|
|
7
|
\(7^3 = 343\)
|
17
|
\(17^3 = 4913\)
|
|
8
|
\(8^3 = 512\)
|
18
|
\(18^3 = 5832\)
|
|
9
|
\(9^3 = 729\)
|
19
|
\(19^3 = 6859\)
|
|
10
|
\(10^3 = 1000\)
|
20
|
\(20^3 = 8000\)
|
1. The cube of every even number is even.
\(2^3 = 8\), \(4^3 = 64\), \(6^3 = 216\), \(8^3 = 512\), ...
Here, \(8\), \(64\), \(216\) and \(512\) are all even numbers.
2. The cube of every odd number is odd.
\(1^3 = 1\), \(3^3 = 27\), \(5^3 = 125\), \(7^3 = 343\), ...
Here, \(1\), \(27\), \(2125\) and \(343\) are all odd numbers.
3. If a natural number ends at \(0\), \(1\), \(4\), \(5\), \(6\) or \(9\), its cube also ends with the same \(0\), \(1\), \(4\), \(5\), \(6\) or \(9\), respectively.
4. The sum of the cubes of first \(n\) natural numbers is equal to the square of their sum.
That is, \(1^3 + 2^3 + 3^3 + 4 ^3 + …. + n^3 = (1 + 2 + 3 + 4 + … + n)^2\)