The definition of a perfect cube is a number that is the result of multiplying an integer by itself three times. In other words, according to Reference.com, it is an integer to the third power. An integer is any positive or negative whole number and zero.
The perfect cube of two, for example, is eight because 2 x 2 x 2 = 8. Other positive perfect cubes include one, 27, 64 and 125. Zero is a perfect cube, and negative perfect cubes include the negatives of the positive perfect cubes. Unlike perfect squares, there is no smallest perfect cube because a negative number multiplied by itself three times is a negative number, and the sequence goes on into infinity. On the other hand, zero is the smallest perfect square because when a negative number is squared, a positive number results.