It's also easy to factor the sum or the difference of two cubes. For example, suppose we need to factor 8x3 + 27. This is the sum of 8x3 (the cube of 2x) and 27 (the cube of 3). So it factors as (2x + 3)(4x2 − 6x + 9). The second factor is the square of the first number being cubed, minus the product of the two numbers, plus the square of the second number.

If instead we had to factor 8x3 − 27, the answer would be (2x − 3)(4x2 + 6x + 9). Note the different signs. Remember, the sign in the linear factor is the same as the sign in the problem. The first sign in the quadratic factor is opposite to the sign in the problem. And the second sign in the quadratic factor is always positive.