$\displaystyle a^3+b^3 = (a+b)(a^2-ab+b^2)$
why is it so?
Why? If you really want to, just go backwards in this manner:
$\displaystyle \begin{aligned}
a^3 + b^3 &= a^3 {\color{red}+ a^2b - a^2b - ab^2 + ab^2} + b^3\;\;\;\text{(adding zero)} \\
&= a^2(a + b) - ab(a + b) + b^2(a + b) \\
&= (a + b)(a^2 - ab + b^2)
\end{aligned}$
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