Answer
$x^6+24x^3+144$
Work Step by Step
Using $(a+b)^2=a^2+2ab+b^2$ or the square of a binomial, the given expression, $
(x^3+12)^2
$, is equivalent to
\begin{array}{l}\require{cancel}
(x^3)^2+2(x^3)(12)+(12)^2
\\\\=
x^6+24x^3+144
.\end{array}