a 3 +b 3

$a^3+b^3 = ~?$

$\small{ \begin{array}{rcl} (a+b)^3 &=& a^3 + 3a^2b+3ab^2 + b^3 \\ (a+b)^3 - 3a^2b - 3ab^2 &=& a^3 + b^3 \\ (a+b)^3 - 3ab ( a+b ) &=& a^3 + b^3 \\ (a+b)[(a+b)^2 - 3ab ] &=& a^3 + b^3 \\ (a+b)( a^2 + 2ab+b^2 - 3ab ) &=& a^3 + b^3 \\ (a+b)( a^2 -ab+b^2 ) &=& a^3 + b^3 \\ \mathbf{a^3 + b^3} & \mathbf{=} & \mathbf{(a+b)( a^2 -ab+b^2 )} \\ \end{array} }$