Is it possible to simplify (2pi^3)/3 - (2pir^3)/(3sqrt.3)
the furthest I was able to go was (2sqrt.3 r^3 - 2pi r^3) / (3sqrt.3)
$\displaystyle \frac{2\pi^{3} }{3} \cdot {\color{blue} \frac{\sqrt{3}}{\sqrt{3}}} \:\: - \:\: \frac{2\pi r^{3}}{3 \sqrt{3}} = \frac{2\pi^{3} \sqrt{3} - 2\pi r^{3}}{3\sqrt{3}}$
Not much else you can do ... unless you factor a bit but that doesn't do a whole lot:
$\displaystyle \frac{2\pi \left(\pi^{2} \sqrt{3} - r^{3}\right)}{3\sqrt{3}}$
Sure:
$\displaystyle \frac{2\pi^{3} \sqrt{3} - 2\pi r^{3}}{3\sqrt{3}} \cdot {\color{blue}\frac{\sqrt{3}}{\sqrt{3}}}$
$\displaystyle = \frac{6\pi^{3} - 2\pi r^{3} \sqrt{3}}{{\color{red}9}}$
Doesn't change it too much. I don't think it matters too much at this point how the expression is represented.
Edited.