If $\mathrm{x}=2+2^{2/3}+2^{1/3}$ then the value of ${\mathrm{x}}^3-6{\mathrm{x}}^2+6\mathrm{x}$ is _______.

Given $\mathrm{x}-2=2^{2/3}+2^{1/3}$

Taking cube of both sides, we get

$\begin{array}{l}(\mathrm{x}-2{)}^3=2^2+2+3\times 2^{2/3}\times 2^{1/3}(\mathrm{x}-2)\\ \Rightarrow (\mathrm{x}-2{)}^3=6+6(\mathrm{x}-2)\end{array}$

or   ${\mathrm{x}}^3-6{\mathrm{x}}^2+12\mathrm{x}-8=-6+6\mathrm{x}$

$\therefore {\mathrm{x}}^3-6{\mathrm{x}}^2+6\mathrm{x}=2$