  Using the previous Belle measurement of the inclusive photon energy in $B\to
X_s\gamma$ decays, we determine the first and second moments of this spectrum
for minimum photon energies in the $B$ meson rest frame ranging from 1.8 to 2.3
GeV. Combining these measurements with recent Belle data on the lepton energy
and hadronic mass moments in $B\to X_c\ell\nu$ decays, we perform fits to
theoretical expressions derived in the 1S and kinetic mass schemes and extract
the magnitude of the Cabibbo-Kobayashi-Maskawa (CKM) matrix element $V_{cb}$,
the $b$-quark mass and other non-perturbative parameters. In the 1S scheme
analysis we find $|V_{cb}|=(41.56\pm 0.68(\mathrm{fit})\pm 0.08(\tau_B))\times
10^{-3}$ and $m_b^\mathrm{1S}=(4.723\pm 0.055)$ GeV. In the kinetic scheme, we
obtain $|V_{cb}|=(41.58\pm 0.69(\mathrm{fit})\pm 0.08(\tau_B)\pm
0.58(\mathrm{th}))\times 10^{-3}$ and $m_b^\mathrm{kin}=(4.543\pm 0.075)$ GeV.
