Answer
$2(3x+1)(9x^2-3x+1)$
Work Step by Step
Factoring the $GCF=
2
,$ the given expression, $
54x^3+2
,$ is equivalent to
\begin{array}{l}
2(27x^3+1)
.\end{array}
Using $a^3+b^3=(a+b)(a^2-ab+b^2)$ or the factoring of 2 cubes, the factored form of the expression, $
2(27x^3+1)
,$ is
\begin{array}{l}
2(3x+1)[ (3x)^2-(3x)(1)+(1)^2]
\\\\=
2(3x+1)(9x^2-3x+1)
.\end{array}