How to know that $a^3+b^3 = (a+b)(a^2-ab+b^2)$ Is there a way of go from $a^3+b^3$ to $(a+b)(a^2-ab+b^2)$ other than know the property by heart?

So I guess the answer to this question is to expand the right-hand side of the equation, although it might not be too clear on how to do this.
It might be clearer if you make the substitution $u=a+b$.  Then the right hand side is:
\begin{align*}
(a+b)(a^2-ab+b^2) & = u(a^2-ab+b^2) \\
& = ua^2-uab+ub^2 \\
& = (a+b)a^2-(a+b)ab+(a+b)b^2 \\
& = a^3+ba^2-a^2b-ab^2+ab^2+b^3 \\
& = a^3+b^3
\end{align*}
using the distributive law (and commutivity).
