\(x+2\sqrt{xy}+y-\left(\sqrt{x}\right)^3-\left(\sqrt{y}\right)^3\)
\(=\left(\sqrt{x}+\sqrt{y}\right)^2-\left(\sqrt{x}+\sqrt{y}\right)\left(x-\sqrt{xy}+y\right)\)
\(=\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)-\left(x-\sqrt{xy}+y\right)\)
\(=\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}-x+\sqrt{xy}-y\right)\)