Difference of Two Powers/Examples/Difference of Two Cubes

Theorem

 * $x^3 - y^3 = \paren {x - y} \paren {x^2 + x y + y^2}$

Proof
From Difference of Two Powers:
 * $\displaystyle a^n - b^n = \paren {a - b} \sum_{j \mathop = 0}^{n - 1} a^{n - j - 1} b^j$

The result follows directly by setting $n = 3$.