  We consider asymptotically-free four-dimensional large-$N$ gauge theories
with massive fermionic and bosonic adjoint matter fields, compactified on
squashed three-spheres, and examine their regularized large-$N$ confined-phase
spectral sums. The analysis is done in the limit of vanishing 't Hooft
coupling, which is justified by taking the size of the compactification
manifold to be small compared to the inverse strong scale $\Lambda^{-1}$. Our
results motivate us to conjecture some universal spectral sum rules for these
large $N$ gauge theories.
