Answer
$(3a-2b)(9a^2+6ab+4)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
27a^3-8b^3
,$ use the factoring of the sum/difference of $2$ cubes.
$\bf{\text{Solution Details:}}$
Using $a^3+b^3=(a+b)(a^2-ab+b^2)$ or $a^3-b^3=(a-b)(a^2+ab+b^2)$ or the factoring of the sum/difference of $2$ cubes, the expression above is equivalent to
\begin{array}{l}\require{cancel}
(3a-2b)[(3a)^2+3a(2b)+(2b)^2]
\\\\=
(3a-2b)(9a^2+6ab+4b^2)
.\end{array}
