If $\displaystyle P=2^{\frac{1}{3}}+2^{\frac{2}{3}}+2$,Find out the value for $\displaystyle p^3-6p^2+6p$?

In this case,

I named $\displaystyle p^{\frac{1}{3}}$=a

Then,

$\displaystyle p^2(p-6)+6p$

$\displaystyle (a+a^2+2)^2(a+a^2-4)+6(a+a^2+2)$

Then I can't solve think i might take long time to solve so please give me another idea to solve this?