Answer
$(t-3)(t^2+3t+9)$
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, $
t^3-27
,$ is
\begin{array}{l}
(t-3)[(t)^2-(t)(-3)+(-3)^2]
\\\\=
(t-3)[t^2+3t+9]
\\\\=
(t-3)(t^2+3t+9)
.\end{array}