In this work, we have investigated the hybridization of plasmon resonance modes in completely copper (Cu)-based subwavelength nanoparticle clusters from simple symmetric dimers to complex asymmetric self-assembled structures. The quality of apparent bonding and antibonding plasmon resonance modes for all of the clusters has been studied, and we examined the spectral response of each one of the proposed configurations numerically using the finite-difference time domain (FDTD) method. The effect of the geometric sizes of nanoparticles used and substrate refractive index on the cross-sectional profiles of each of the studied structures has been calculated and drawn. We proved that Fano-like resonance can be formed in Cu-based heptamer clusters as in analogous noble metallic particles (e.g., Au and Ag) by determining the coupling strength and interference between sub-radiant and super-radiant resonance modes. Employing certain Cu nanodiscs in designing an octamer structure, we measured the quality of the Fano dip formation along the scattering diagram. Accurate tuning of the geometric sizes for the Cu-based octamer yields an opportunity to observe isotropic, deep, and narrow Fano minima along the scattering profile that are in comparable condition with the response of other plasmonic metallic substances. Immersing investigated final Cu-based octamer in various liquids with different refractive indices, we determined the sensing accuracy of the cluster based on the performance of the Fano dip. Plotting a linear diagram of plasmon energy differences over the refractive index variations as a figure of merit (FoM), which we have quantified as 13.25. With this method, the precision of the completely Cu-based octamer is verified numerically using the FDTD tool. This study paves the way toward the use of Cu as an efficient, low-cost, and complementary metal-oxide semiconductor (CMOS)-compatible plasmonic material with optical properties that are similar to analogous plasmonic substances.