Cube Number
When a number is multiplied by itself three times, the result is called a cube number (or perfect cube).
In general, for any number \(n\), we write the cube \(n\times n\times n\) as \(n^3\).
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 consists of cube numbers of the first twenty numbers.
| Number | Cube Number | Number | Cube Number |
| \(1\) | \(1^3 =1\) | \(11\) | \(11^3 = 1331\) |
| \(2\) | \(2^3 = 8\) | \(12\) | \(12^3 = 1728\) |
| \(3\) | \(3^3 = 27\) | \(13\) | \(13^3 = 2197\) |
| \(4\) | \(4^3 = 64\) | \(14\) | \(14^3 = 2744\) |
| \(5\) | \(5^3 = 125\) | \(15\) | \(15^3 = 3375\) |
| \(6\) | \(6^3 = 216\) | \(16\) | \(16^3 = 4096\) |
| \(7\) | \(7^3 = 343\) | \(17\) | \(17^3 = 4913\) |
| \(8\) | \(8^3 = 512\) | \(18\) | \(18^3 = 5832\) |
| \(9\) | \(9^3 = 729\) | \(19\) | \(19^3 = 6859\) |
| \(10\) | \(10^3 = 1000\) | \(20\) | \(20^3 = 8000\) |
Properties of cube numbers:
1. Unit digits of cubes
| Unit digit of \(n\) | Unit digit of \(n^3\) |
| \(0\) | \(0\) |
| \(1\) | \(1\) |
| \(2\) | \(8\) |
| \(3\) | \(7\) |
| \(4\) | \(4\) |
| \(5\) | \(5\) |
| \(6\) | \(6\) |
| \(7\) | \(3\) |
| \(8\) | \(2\) |
| \(9\) | \(9\) |
2. The cube of a positive number is always positive.
Example:
\(4^3 = 4\times 4\times 4 = 64\)
3. The cube of a negative number is always negative.
Example:
\((-4)^3 = (-4)\times (-4) \times (-4) = -64\)
4. The cube of every even number is even.
Example:
\(2^3 = 8\), \(4^3 = 64\), \(6^3 = 216\),...
Here, \(8\), \(64\) and \(216\) are all even numbers.
5. The cube of every odd number is odd.
Example:
\(1^3 = 1\), \(3^3 = 27\), \(5^3 = 125\)
Here, \(1\), \(27\) and \(125\) are all odd numbers.
6. When cubing a fraction number, cube both the numerator and the denominator separately.
Example:
\(\left(\frac{4}{5}\right)^3 = \frac{4}{5} \times\frac{4}{5} \times \frac{4}{5} = \frac{64}{125}\)
7. When cubing a decimal number, the number of decimal places in the answer will be three times the number of decimal places in the original number.
Example:
\((13.08)^3 = 13.08\times 13.08\times 13.08 = 2237.810112\)
8. A perfect cube does not end with two zeros; the number of zeros at the end of \(n^3\) is always a multiple of \(3\).
Example:
\(10^3 = 1000\), \(20^3 = 8000\), \(500^3 = 125000000\).
Reference:
National Council of Educational Research and Training (2025). Math - Standard 8. Ganita Prakash, Part I. A square and a cube - 1.2 Cube Number (pg. 11-13). Published at the Publication Division by the Secretary, National Council of Educational Research and Training, Sri Aurobindo Marg, New Delhi.