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