Cube numbers are the product of an integer multiplied by itself, and then by itself again. A cube number is the product of a base number, n, to the third power, written exponentially as n^3. For example, 4 x 4 x 4, or 4^3, yields the cube 64. All positive numbers raised to the third power have positive cubes. Negative numbers raised to the third power, however, have negative cubes. Two negative numbers multiplied together have a positive product, but when that product is multiplied by the negative number again, the answer is negative. For example, -4 x -4 x -4, or -4^3, equals -64.

It is not possible to name the very first 10 cubes, because negative numbers are infinite. There is, therefore, no smallest cube. In the number sequence that includes odd integers beginning with one, the first number, one, is a cube. Adding the next two numbers, three and five, yields the second cube, which is eight. The sum of the next three numbers in the sequence, seven, nine and 11, is the next cube, 27. The pattern continues.