Consider $64x^{3}+1$. Rewrite $64x^{3}+1$ as $\left(4x\right)^{3}+1^{3}$. The sum of cubes can be factored using the rule: $a^{3}+b^{3}=\left(a+b\right)\left(a^{2}-ab+b^{2}\right)$.
$$\left(4x+1\right)\left(16x^{2}-4x+1\right)$$
Rewrite the complete factored expression. Polynomial $16x^{2}-4x+1$ is not factored since it does not have any rational roots.
