  We derive analytic results for scalar massless bosonic vacuum sum-integrals
at two loops. Building upon a recent factorization proof of massive two-loop
vacuum integrals, we are able to solve the corresponding Matsubara sums and map
the result onto one-loop structures, thereby proving factorization also in the
sum-integral setting. Analytic results are provided for generic integer-valued
propagator- and numerator-powers of the class of sum-integrals under
consideration, allowing to eliminate them from any perturbative expansion,
dramatically simplifying the evaluation of some observables encountered e.g. in
hot QCD.
