Sum of Two Odd Powers/Examples/Sum of Two Cubes

Theorem

 * $x^3 + y^3 = \left({x + y}\right) \left({x^2 - x y + y^2}\right)$

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

Let $x = a$ and $y = -b$.

Then: