  We continue to study frequency-dependent complex bulk viscosities of
one-dimensional Bose and Fermi gases with contact interactions, which exhibit
the weak-strong duality according to our recent work. Here we show that they
are contributed to by Drude peaks divergent at zero frequency as typical for
transport coefficients of quantum integrable systems in one dimension. In
particular, their Drude weights are evaluated based on the Kubo formula in the
high-temperature limit at arbitrary coupling as well as in the weak-coupling
and strong-coupling limits at arbitrary temperature, where systematic
expansions in terms of small parameters are available. In all three limits, the
Drude peaks are found at higher orders compared to the finite regular parts.
