The CUPID Collaboration is designing a tonne-scale, background-free detector to search for double beta decay with sufficient sensitivity to fully explore the parameter space corresponding to the inverted neutrino mass hierarchy scenario. One of the CUPID demonstrators, CUPID-Mo, has proved the potential of enriched Li$_{2}$$^{100}$MoO$_4$ crystals as suitable detectors for neutrinoless double beta decay search. In this work, we characterised cubic crystals that, compared to the cylindrical crystals used by CUPID-Mo, are more appealing for the construction of tightly packed arrays. We measured an average energy resolution of (6.7$pm$0.6) keV FWHM in the region of interest, approaching the CUPID target of 5 keV FWHM. We assessed the identification of $alpha$ particles with and without a reflecting foil that enhances the scintillation light collection efficiency, proving that the baseline design of CUPID already ensures a complete suppression of this $alpha$-induced background contribution. We also used the collected data to validate a Monte Carlo simulation modelling the light collection efficiency, which will enable further optimisations of the detector.
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