We present measurements of the first to fourth moments of the lepton mass squared q2 of B→Xcℓν¯ℓ decays for ℓ=e, μ and with Xc a hadronic system containing a charm quark. These results use a sample of electron-positron collisions at the ϒ(4S) resonance corresponding to 62.8 fb-1 of integrated luminosity and collected by the Belle II 2 experiment in 2019 and 2020. To identify the Xc system and reconstruct q2, one of the B mesons from an ϒ(4S)→BB¯ decay is fully reconstructed in a hadronic decay mode using a multivariate B tagging algorithm. We report raw and central moments for q2>1.5 GeV2/c4 up to q2>8.5 GeV2/c4, probing up to 77% of the accessible B→Xcℓν¯ℓ phase space. This is the first measurement of moments in the experimentally challenging range of [1.5,2.5] GeV2/c4. The results can be used for a new determination of |Vcb| using inclusive B→Xcℓν¯ℓ decays. © 2023 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.