A scintillating bolometer based on a large cubic Li$_{2}$$^{100}$MoO$_4$ crystal (45 mm side) and a Ge wafer (scintillation detector) has been operated in the CROSS cryogenic facility at the Canfranc underground laboratory in Spain. The dual-readout detector is a prototype of the technology that will be used in the next-generation $0\nu2\beta$ experiment CUPID. The measurements were performed at 18 and 12 mK temperature in a pulse tube dilution refrigerator. This setup utilizes the same technology as the CUORE cryostat that will host CUPID and so represents an accurate estimation of the expected performance. The Li$_{2}$$^{100}$MoO$_4$ bolometer shows a high energy resolution of 6 keV FWHM at the 2615 keV $\gamma$ line. The detection of scintillation light for each event triggered by the Li$_{2}$$^{100}$MoO$_4$ bolometer allowed for a full separation ($\sim$8$\sigma$) between $\gamma$($\beta$) and $\alpha$ events above 2 MeV. The Li$_{2}$$^{100}$MoO$_4$ crystal also shows a high internal radiopurity with $^{228}$Th and $^{226}$Ra activities of less than 3 and 8 $\mu$Bq/kg, respectively. Taking also into account the advantage of a more compact and massive detector array, which can be made of cubic-shaped crystals (compared to the cylindrical ones), this test demonstrates the great potential of cubic Li$_{2}$$^{100}$MoO$_4$ scintillating bolometers for high-sensitivity searches for the $^{100}$Mo $0\nu2\beta$ decay in CROSS and CUPID projects.