Cube Numbers – Multiplying a Number by Itself Twice

A cube number is what you get when a whole number is multiplied by itself twice more: n³ = n × n × n. The first few are 1, 8, 27, 64, 125… and just like square numbers get their name from a flat square grid, cube numbers get their name from a genuine 3D cube: if you stack that many identical small cubes into a bigger cube shape, the side length is exactly the number you cubed – 27 unit cubes stack perfectly into a 3×3×3 cube, which is exactly why 3³ = 27.

The Pattern of Cube Numbers

Cubing means multiplying a number by itself three times in total: n³ = n × n × n. The first few cube numbers are 1, 8, 27, 64, 125, 216…

Find 6 cubed.

6³ = 6 × 6 × 6 = 216.

Recognising Cube Numbers

Is 100 a cube number?

The nearest cube numbers are 64 (4³) and 125 (5³). 100 sits between them, so it is not a cube number.

Real-Life Application

Volume: the volume of a cube with side n is n³.
Packing: stacking identical boxes into a larger cube shape.
Dice and puzzle cubes: a Rubik's Cube has 3³ = 27 small cube positions.

Key Takeaways

A cube number is n × n × n for a whole number n.
The name comes from the volume of a 3D cube with that many stacked unit cubes.
Cube roots, covered later in this section, are the reverse operation.

Practice: Cube Numbers

Find the Cube Number