Cubed

Cubed refers to the operation of raising a number to the third power, or to something shaped like a cube. In mathematics, to cube a number means multiply the number by itself three times: x^3 = x × x × x. The result is called the cube of x. A number that is the cube of an integer is a cube number (a perfect cube). Examples include 0^3 = 0, 1^3 = 1, 2^3 = 8, 3^3 = 27, 4^3 = 64, and 5^3 = 125. Negative numbers cubed remain negative: (−2)^3 = −8.

Cube numbers have several algebraic properties. For any numbers a and b, (ab)^3 = a^3 b^3. The expansion of a cube of a sum is (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3. The cube function is strictly increasing over the real numbers, and its derivative is 3x^2. The inverse operation is the cube root, denoted ∛x.

Geometrically, a cube is a regular hexahedron with six equal square faces. If a cube has side length s, its volume equals s^3 and its surface area equals 6s^2. In everyday language, “cubed” may describe an object shaped like a cube or composed of unit cubes (for example, a cube-shaped sugar piece or a three-dimensional array built from unit cubes).

The term remains common in math education to describe the power operation, often written with the exponent 3 after a number, as in seven cubed equals 343.