In simple terms, when a number $a$ is multiplied by itself three times, the product is called the cube of $a$.
Mathematically, we write this as:
You can read $a^3$ as “$a$ cubed” or “$a$ raised to the power of 3.”
Memorizing the cubes of the first ten natural numbers is a great way to speed up your mental math. Here is a quick reference table:
| Number (n) | Calculation | Cube (n3) |
| 1 | $1 \times 1 \times 1$ | 1 |
| 2 | $2 \times 2 \times 2$ | 8 |
| 3 | $3 \times 3 \times 3$ | 27 |
| 4 | $4 \times 4 \times 4$ | 64 |
| 5 | $5 \times 5 \times 5$ | 125 |
| 6 | $6 \times 6 \times 6$ | 216 |
| 7 | – | 343 |
| 8 | – | 512 |
| 9 | – | 729 |
| 10 | – | 1000 |
A common question students ask is: “Can you cube a negative number?” The answer is yes, but there is a specific rule to follow.
Key Rule: The cube of a negative number is always negative.
Formula: $(-a)^3 = -a^3$
This happens because you are multiplying three negative signs together. Since a negative times a negative is a positive, and that positive times a third negative results in a negative, the final answer remains “minus.”
$(-1)^3 = -1 \times -1 \times -1 = -1$
$(-2)^3 = -2 \times -2 \times -2 = -8$
$(-3)^3 = -27$
$(-4)^3 = -64$