Theory:

Do you ever heard the word cube before?
 
Yes, we know that a cube is a \(3\)-dimensional figure; we already studied it in earlier classes.
 
Recall:
A cube is a solid figure, which has all sides of equal length.
 
cube_vol (1).png
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
\(20^3 = 8000\)