Consider $125m^{3}-1$. Rewrite $125m^{3}-1$ as $\left(5m\right)^{3}-1^{3}$. The difference of cubes can be factored using the rule: $a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right)$.
$$\left(5m-1\right)\left(25m^{2}+5m+1\right)$$
Rewrite the complete factored expression. Polynomial $25m^{2}+5m+1$ is not factored since it does not have any rational roots.
