If a, b, c are the roots of the equation  $x^3-3x^2+3x+7=0$, then the value of  $\left|\begin{array}{ccc}2bc-a^2& c^2& b^2\\ c^2& 2ac-b^2& a^2\\ b^2& a^2& 2ab-c^2\end{array}\right|$ is equal to _______

$$\begin{gathered} {(x-1)}^3=-8\Rightarrow x-1=-2,-2\omega ,-2{\omega }^2 \\ \Rightarrow x=-1,1-2\omega ,1-2{\omega }^2 \\ \therefore a=-1,b=1-2\omega ,c=1-2{\omega }^2 \\ \because \left|\begin{array}{ccc}a& b& c^2\\ b& c& c\\ c& a& b\end{array}\right|=\left|\begin{array}{ccc}a& b& c\\ b& c& a\\ c& a& b\end{array}\right|=\left|\begin{array}{ccc}-a& c& b\\ -b& a& c\\ -c& b& a\end{array}\right|=\left|\begin{array}{ccc}2bc-a^2& c^2& b^2\\ c^2& 2ac-b^2& a^2\\ b^2& a^2& 2ab-c^2\end{array}\right| \end{gathered}$$