  The contribution of vortex core has been taken into account properly in
constructing a torque theory for multiband superconductors. We employ the
prescription of describing internal magnetic field in the vortex lattice by Hao
{\it et al.} and by Yaouanc {\it et al.} to derive a torque formula as a
natural extension of a preceding London theory. In marked contrast with the
preceding model, our novel formula does not contain a phenomenological
parameter $\eta$, which prevents us from obtaining a {\it true} upper critical
field $H_{\rm c2}$ by analyzing an experimental torque curve. The parameter
$\eta$ was originally introduced to take care of the uncertainty in determining
the vortex core size $\xi_v$. Furthermore, we reveal that the $\eta$ value is
universally scaled by anisotropy $\gamma$, magnetic field $B$, and $H_{\rm c2}$
due to field dependence of $\xi_v$. This may revitalize the single-band Kogan
model in combination with a universal function $\eta(\gamma, B, H_{\rm c2})$
instead of a constant $\eta$.
