Answer
$a^6+12a^3+36$
Work Step by Step
Using $(a+b)^2=a^2+2ab+b^2$ or the square of a binomial, the given expression, $
\left( a^3+6 \right)^2
$, is equivalent to
\begin{array}{l}\require{cancel}
(a^3)^2+2(a^3)\left( 6 \right)+\left( 6 \right)^2
\\\\=
a^6+12a^3+36
.\end{array}