Plasmonic nanocavities have the ability to confine light in extremely small volumes. They are receiving increased attention from the nanophotonics and nanoelectronics communities due to their potential applications in optoelectronics, quantum optics, and novel nanophotonic and plasmonic-circuit devices. The coupling of colloidal plasmonic nanocrystals to metal films provides an inexpensive approach to fabricate a virtually unlimited number of individual resonators that can be tuned by adjusting nanoparticle size, gap thickness and refractive index. In this study, we focus on silver nanocubes separated from a gold mirror by thin amorphous dielectric layers (Al2O3, TiO2). We measure the optical response and perform correlative SEM microscopy on a large number (>800) of individual resonators to unveil the statistical distribution of gap plasmon modes and assess systematically the impact that various parameters, such as dielectric thickness, refractive index and nanocube size, have on the resonator sensitivity. The sensitivity of the fundamental mode can be as large as 8 nm/nm for nanocube size variation, 50 nm/nm for Al2O3 thickness variation and 130 nm/RIU for index change of the spacer layer. With the help of numerical simulations this approach enables to infer a quantitative statistical distribution of molecular coatings present on the nanocubes surface, such as polyvinylpyrrolidone, which can affect performance of nanoelectronic devices and assess the strategy to remove it. Finally, by performing measurements on annealed TiO2 layers (2-4nm), we observe an unexpected splitting of the fundamental resonance into two modes. Polarization-resolved measurements enable us to associate this phenomenon to a birefringent behavior of the system.