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.