Answer
$\sqrt[3]{a^2}+4\sqrt[3]{a}+4$
Work Step by Step
Using $(a+b)^2=a^2+2ab+b^2$ , the expression $
(\sqrt[3]{a}+2)^2
$ simplifies to
\begin{array}{l}
(\sqrt[3]{a})^2+2(\sqrt[3]{a})(2)+(2)^2
\\=
\sqrt[3]{a^2}+4\sqrt[3]{a}+4
.\end{array}