Consider $1+m^{3}$. Rewrite $1+m^{3}$ as $m^{3}+1^{3}$. The sum of cubes can be factored using the rule: $a^{3}+b^{3}=\left(a+b\right)\left(a^{2}-ab+b^{2}\right)$.
$$\left(m+1\right)\left(m^{2}-m+1\right)$$
Rewrite the complete factored expression. Polynomial $m^{2}-m+1$ is not factored since it does not have any rational roots.
