We carried out the near-field optical imaging of isolated and dimerized gold nanocubes to directly investigate the strong coupling between two adjacent nanoparticles. The high-resolution (approximately 10 nm) local field maps (intensities and phases) of self-assembled nanocube dimers reveal antisymmetric plasmon modes that are starkly different from a simple superposition of two monomeric dipole plasmons, which is fully reproduced by the electrodynamics simulations. The result decisively proves that, for the closely spaced pair of nanoparticles (interparticle distance/particle size approximately 0.04), the strong Coulombic attraction between the charges at the interparticle gap dominates over the intraparticle charge oscillations, resulting in a hybridized dimer plasmon mode that is qualitatively different from those expected from a simple dipole-dipole coupling model.