Find the following product:
$\left(\frac{x}{2}+2 y\right)\left(\frac{x^{2}}{4}-x y+4 y^{2}\right)$

(N/A) The given expression is of the form $(a+b)(a^2-ab+b^2)$,where $a = \frac{x}{2}$ and $b = 2y$.
Using the algebraic identity $(a+b)(a^2-ab+b^2) = a^3+b^3$:
$\left(\frac{x}{2}+2 y\right)\left\{\left(\frac{x}{2}\right)^{2}-\left(\frac{x}{2}\right)(2 y)+(2 y)^{2}\right\} = \left(\frac{x}{2}\right)^{3}+(2 y)^{3}$
$= \frac{x^3}{8} + 8y^3$