Eigenvalue sum after a shift, inverse and cube

A square matrix $A$ (size $n\times n$) has exactly the eigenvalues $5$ and $7$. Define $B=\left((A-3I_n)^{-1}\right)^3$. What is the sum of the eigenvalues of $B$ (each distinct eigenvalue counted once)?

$9/64$. Subtracting $3I$ moves the eigenvalues to $2$ and $4$; inverting takes reciprocals, $\tfrac12$ and $\tfrac14$; cubing gives $\tfrac18$ and $\tfrac1{64}$, which add to $\tfrac{9}{64}$.