We report on silver nanocubes (AgNCs) infiltrated into cylindrical nanopores of porous alumina membranes (PAM) with an outstanding chemical sensitivity based on refractive index sensing (RIS) measurements. Numerical simulations performed using the finite-difference time-domain (FDTD) method suggested that the enhanced sensitivity is based mainly on the inter-pore coupling plasmonic effect. This effect is related to plasmonic amplification based on localized surface plasmon resonance (LSPR) coupling between AgNCs located at the pore walls of neighboring cylindrical pores and separated by a nanoscale wall. Results are discussed for different aggregation scenarios ranging from individual nanocubes through pentamers on a flat glass surface, a flat alumina surface, and a concave local shape representing the experimental conditions. An experimental RIS sensitivity of about 770 nm per refractive index unit was found to be more than an order of magnitude higher for silver nanocube aggregates within cylindrical pores than that observed for ordinary planar substrates.