Answer
$(3a-2)(9a^2+6a+4)$
Work Step by Step
Using $(a)^3-(b)^3=(a-b)(a^2+ab+b^2)$ or the factoring of the difference of two cubes, the given expression, $
27a^3-8
,$ is equivalent to
\begin{align*}
&
(3a)^3-(2)^3
\\&=
(3a-2)[(3a)^2+(3a)(2)+(2)^2]
\\&=
(3a-2)(9a^2+6a+4)
.\end{align*}
Hence, the expression $27a^3-8$ is equivalent to $(3a-2)(9a^2+6a+4)$.
