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