If $x^2+x+1=0 $, then find the value of $(x^3+1/x^3)^3$? 
If $x^2+x+1=0 $, then find the value of $(x^3+1/x^3)^3$

This thing doesn't make sense how should I use first identity to find the second one.

$x^3-1 = (x-1)(x^2+x+1) = 0$, so $x^3=1$. That's all you need.
