Answer
$(3x+1)(9x^2-3x+1)$
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, $
27x^3+1
,$ is
\begin{array}{l}
(3x+1)[(3x)^2-(3x)(1)+(1)^2]
\\\\=
(3x+1)(9x^2-3x+1)
.\end{array}