Answer
$(2x+3)(4x^2 -6x +9)$
Work Step by Step
Since $8x^3+27$ is a sum of the two cubes $(2x)^3$ and $3^3$, then by making use of the sumof two cubes
$$a^3 +b^3 = (a + b)(a^2 -ab + b^2),$$
we have
\begin{align*}
8x^3+27&=(2x)^3+3^3\\
&= (2x+3)[(2x)^2 -2x(3) + 3^2]\\
&= ( 2x+3)(4x^2 -6x +9)
\end{align*}
