Consider $8x^{3}-27$. Rewrite $8x^{3}-27$ as $\left(2x\right)^{3}-3^{3}$. The difference of cubes can be factored using the rule: $a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right)$.
$$\left(2x-3\right)\left(4x^{2}+6x+9\right)$$
Rewrite the complete factored expression. Polynomial $4x^{2}+6x+9$ is not factored since it does not have any rational roots.
