Answer
$(2t+1)(4t^2-2t+1)$
Work Step by Step
Using $a^3+b^3=(a+b)(a^2-ab+b^2)$ or the factoring of $2$ cubes, then the factored form of the given expression, $
8t^3+1
$ is
\begin{array}{l}
(2t+1)[(2t)^2-(2t)(1)+(1)^2]
\\\\=
(2t+1)(4t^2-2t+1)
.\end{array}