Cubic Numbers

What is a Cube?

A cube number is obtained by multiplying a number by itself three times: $n^3 = n \times n \times n$. Geometrically, it represents the volume of a cube.

Hardy-Ramanujan Number: 1729

1729 is known as the Taxicab Number. It is the smallest number that can be expressed as the sum of two cubes in two different ways.

Properties of Cubes

1. Parity: Cube of an even number is even ($2^3 = 8$). Cube of an odd number is odd ($3^3 = 27$).
2. Last Digits:
   • If a number ends in 1, its cube ends in 1.
   • If a number ends in 2, its cube ends in 8.
   • If a number ends in 3, its cube ends in 7.
   • If a number ends in 4, its cube ends in 4.
   • If a number ends in 5, its cube ends in 5.
   • If a number ends in 6, its cube ends in 6.
   • If a number ends in 7, its cube ends in 3.
   • If a number ends in 8, its cube ends in 2.
   • If a number ends in 9, its cube ends in 9.
   • If a number ends in 0, its cube ends in 0.