Answer
$a+64$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To multiply the given expression, $
(\sqrt[3]{a}+4)(\sqrt[3]{a^2}-4\sqrt[3]{a}+16)
,$ use the concept on factoring the sum of $2$ cubes.
$\bf{\text{Solution Details:}}$
Using the factoring of the sum of $2$ cubes which is given by $a^3+b^3=(a+b)(a^2-ab+b^2)$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
(\sqrt[3]{a})^3+(4)^3
\\\\=
a+64
.\end{array}
