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