Simplify: $\;$ $\dfrac{\left(\sqrt{a^3} + \sqrt{b^3}\right)}{\sqrt[3]{a^2 \left(a - b\right)^2}} \times \dfrac{a^{\frac{2}{3}} \left(\sqrt{a^3} - \sqrt{b^3}\right)}{\left(a - b\right)^{\frac{1}{3}}}$
$\dfrac{\left(\sqrt{a^3} + \sqrt{b^3}\right)}{\sqrt[3]{a^2 \left(a - b\right)^2}} \times \dfrac{a^{\frac{2}{3}} \left(\sqrt{a^3} - \sqrt{b^3}\right)}{\left(a - b\right)^{\frac{1}{3}}}$
$= \dfrac{\left(a^3 - b^3\right) a^{\frac{2}{3}}}{a^{\frac{2}{3}} \left(a - b\right)^{\frac{2}{3}} \left(a - b\right)^{\frac{1}{3}}}$
$= \dfrac{\left(a - b\right) \left(a^2 + ab + b^2\right)}{a - b}$
$= a^2 + ab + b^2$