Consider $a^{6}-2a^{3}b^{3}+b^{6}$ as a polynomial over variable $a$.
$$a^{6}-2b^{3}a^{3}+b^{6}$$
Find one factor of the form $a^{k}+m$, where $a^{k}$ divides the monomial with the highest power $a^{6}$ and $m$ divides the constant factor $b^{6}$. One such factor is $a^{3}-b^{3}$. Factor the polynomial by dividing it by this factor.
