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On the basis of recently computed nonlinear convective pulsation models of Galactic Cepheids, spanning wide ranges of input stellar parameters, we derive theoretical mass-dependent Period-Wesenheit relations in the Gaia bands, namely $G$, $G_{BP}$ and $G_{RP}$, that are found to be almost independent of the assumed efficiency of super-adiabatic convection. The application to a selected sub-sample of Gaia Data Release 2 Galactic Cepheids database allows us to derive mass-dependent estimates of their individual distances. By imposing their match with the astrometric values inferred from Gaia, we are able to evaluate the individual mass of each pulsator. The inferred mass distribution is peaked around 5.6$M_{\odot}$ and 5.4$M_{\odot}$ for the F and FO pulsators, respectively. If the estimated Gaia parallax offset $<Δ\varpi>$=0.046 mas is applied to Gaia parallaxes before imposing their coincidence with the theoretical ones, the inferred mass distribution is found to shift towards lower masses, namely $\sim$5.2$M_{\odot}$ and 5.1$M_{\odot}$ for the F and FO pulsators, respectively. The comparison with independent evaluations of the stellar masses, for a subset of binary Cepheids in our sample, seems to support the predictive capability of current theoretical scenario. By forcing the coincidence of our mass determinations with these literature values we derive an independent estimate of the mean offset to be applied to Gaia DR2 parallaxes, $<Δ\varpi>$=0.053 $\pm$ 0.029 mas, slightly higher but in agreement within the errors with Riess2018 value.