Difference of two cubes
= Difference of two cubes
{title2=$a^3-b^3=(a-b)(a^2+ab+b^2)$}
The <polynomial identity>
$$
\boxed{a^3-b^3=(a-b)(a^2+ab+b^2)}
$$
follows by multiplying out the right side. For real $a,b$, the quadratic factor is $a^2+ab+b^2=(a+b/2)^2+3b^2/4$, so it is nonnegative and vanishes only when $a=b=0$. The identity is a special case of the <finite geometric series> factorisation $a^n-b^n=(a-b)\sum_{j=0}^{n-1}a^{n-1-j}b^j$.