Sum of two cubes
= Sum of two cubes
{title2=$a^3+b^3=(a+b)(a^2-ab+b^2)$}
Replacing $b$ by $-b$ in the <difference of two cubes> gives
$$
\boxed{a^3+b^3=(a+b)(a^2-ab+b^2).}
$$
For real cube roots $u=a^{1/3}$ and $v=b^{1/3}$, this simplifies $(a^{1/3}+b^{1/3})(a^{2/3}-(ab)^{1/3}+b^{2/3})$ to $a+b$. Specifying real cube roots matters when using such identities with negative real inputs; unconstrained <complex exponentiation> has logarithm-branch choices.