Plasmonic nanocomposites based on well-dispersed silver nanocubes in poly(vinylpyrrolidone) are presented that are solution-processed into layers of varying volume fractions of nanocubes. We show that the high-energy modes of the nanocubes are almost insensitive to plasmonic coupling within the nanocube assemblies, leading to a linear increase in light absorption in the UV region with the nanocube densities. Concerning the main dipolar resonance mode at 450 nm, it is strongly affected by the formation of these assemblies, leading to an increased absorption in the UV region as well as a large absorption band in the visible region. Simulations of the optical response of the nanocube assemblies as a function of nanocube spacing and electric field polarization reveal that optical features in the visible region are due to intercube couplings at short intercube distances and parallel electric field orientation. In contrast, the additional plasmonic band in the UV region has its origin in residual dipolar oscillations of the nanocubes in combination with weak dipolar coupling for both parallel and transversal field polarizations. The combination of these effects leads to an enlarged absorption band in the UV region with nearly perfect light absorption of 98.8% at a high silver volume fraction of 8% that is accompanied by a very weak specular reflection of only 0.28%. Although such perfect absorption is usually observed only when nanocubes are assembled on a gold surface, nearly perfect absorption herein is achieved on a large palette of substrates including glass, plastic, and cheap metals such as aluminum, making it a promising approach for solution-processed robust and cheap quasi-perfect absorption coatings.