Cubed — Definition, Formula & Examples

Cubed means a number is raised to the third power. For example, 4 cubed means

4 \times 4 \times 4

, which equals 64.

To cube a number $a$ is to compute $a^3 = a \times a \times a$ . The result is called the cube of $a$ , and the operation corresponds to exponentiation with an exponent of 3.

Key Formula

a^3 = a \times a \times a

Where:

$a$ = The base number being cubed

How It Works

When you see the word "cubed" or the exponent 3, you multiply the base number by itself three times. The name comes from geometry: the volume of a cube with side length

s

s^3

. Cubing works with any real number — positive, negative, or fractional. Cubing a negative number gives a negative result because an odd number of negative factors produces a negative product.

Worked Example

Problem: Find the value of 5 cubed.

Write the expression: "5 cubed" means 5 raised to the third power.

5^3

Multiply step by step: Multiply 5 by itself, then by 5 again.

5 \times 5 = 25, \quad 25 \times 5 = 125

Answer:

5^3 = 125

Why It Matters

Cubing appears whenever you calculate the volume of a cube or sphere. In algebra and pre-algebra, recognizing perfect cubes like 8, 27, 64, and 125 helps you factor expressions and simplify cube roots.

Common Mistakes

Mistake: Confusing cubed with tripled — thinking

4^3

means

4 \times 3 = 12

Correction: Cubing means multiplying the number by itself three times (

4 \times 4 \times 4 = 64

), not multiplying it by 3.