All About Numbers
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…
Just as a square number is the area of a flat square, a cube number is the volume of a solid cube. 5³ = 125 is exactly how many unit cubes it takes to fill a 5-by-5-by-5 cube.
6³ = 6 × 6 × 6 = 216.
Recognising Cube Numbers
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.