Answer
$(3-2t)(9+6t+4t^2)$
Work Step by Step
Using $a^3+b^3=(a+b)(a^2-ab+b^2)$ or the factoring of 2 cubes, the factored form of the given expression, $
27-8t^3
,$ is
\begin{array}{l}
(3-2t)[(3)^2-(3)(-2t)+(-2t)^2]
\\\\=
(3-2t)(9+6t+4t^2)
.\end{array}