  We present the measurement of the first to fourth order moments of the
four-momentum transfer squared, $q^2$, of inclusive $B \rightarrow X_c \ell^+
\nu_{\ell}$ decays using the full Belle data set of 711 $\mathrm{fb}^{-1}$ of
integrated luminosity at the $\Upsilon(4S)$ resonance where $\ell = e, \mu$.
The determination of these moments and their systematic uncertainties open new
pathways to determine the absolute value of the CKM matrix element $V_{cb}$
using a reduced set of matrix elements of the heavy quark expansion. In order
to identify and reconstruct the $X_c$ system, we reconstruct one of the two
$B$-mesons using machine learning techniques in fully hadronic decay modes. The
moments are measured with progressively increasing threshold selections on
$q^2$ starting with a lower value of 3.0 $\mathrm{GeV}^2$ in steps of 0.5
$\mathrm{GeV}^2$ up to a value of 10.0 $\mathrm{GeV}^2$. The measured moments
are further unfolded, correcting for reconstruction and selection effects as
well as QED final state radiation. We report the moments separately for
electron and muon final states and observe no lepton flavor universality
violating effects.
