Matrices And Determinants

For some $\alpha, \beta \in \mathbf{R}$, let $A=\left[\begin{array}{ll}\alpha & 2 \\ 1 & 2\end{array}\right]$ and $B=\left[\begin{array}{ll}1 & 1 \\ 1 & \beta\end{array}\right]$ be such that $A^2-4 A+2 I=B^2-3 B+I=O$. Then $\left(\operatorname{det}\left(\operatorname{adj}\left(A^3-B^3\right)\right)\right)^2$ is equal to $\_\_\_\_$ .