  Closed simple integral representation through Vogel's universal parameters is
found both for perturbative and nonperturbative (which is inverse invariant
group volume) parts of free energy of Chern-Simons theory on $S^3$. This proves
the universality of that partition function. For classical groups it manifestly
satisfy N \rightarrow -N duality, in apparent contradiction with previously
used ones. For SU(N) we show that asymptotic of nonperturbative part of our
partition function coincides with that of Barnes G-function, recover
Chern-Simons/topological string duality in genus expansion and resolve
abovementioned contradiction. We discuss few possible directions of development
of these results: derivation of representation of free energy through
Gopakumar-Vafa invariants, possible appearance of non-perturbative additional
terms, 1/N expansion for exceptional groups, duality between string coupling
constant and K\"ahler parameters, etc.
