Sum or Difference of Cubes
A polynomial in the form a ^{3} + b ^{3} is called a sum of cubes. A polynomial in the form a ^{3} – b ^{3} is called a difference of cubes.
Both of these polynomials have similar factored patterns:

A sum of cubes:

A difference of cubes:
Example 1
Factor x ^{3} + 125.
Example 2
Factor 8 x ^{3} – 27.
Example 3
Factor 2 x ^{3} + 128 y ^{3}.
First find the GCF. GCF = 2
Example 4
Factor x ^{6} – y ^{6}.
First, notice that x ^{6} – y ^{6} is both a difference of squares and a difference of cubes.
In general, factor a difference of squares before factoring a difference of cubes.