Consider $a^{3}-8$. Rewrite $a^{3}-8$ as $a^{3}-2^{3}$. The difference of cubes can be factored using the rule: $p^{3}-q^{3}=\left(p-q\right)\left(p^{2}+pq+q^{2}\right)$.
$$\left(a-2\right)\left(a^{2}+2a+4\right)$$
Rewrite the complete factored expression. Polynomial $a^{2}+2a+4$ is not factored since it does not have any rational roots.
