In the process of searching for the plasmonic modes, various responses of the system for external fields are used to observe plasmons. However, these methods exist an obvious shortage. This is that some plasmonic modes may not have been found due they are not excited by the external fields. Recently, in two-dimensional square atomic clusters, we have presented the eigenequations of plasmon to study plasmons, and find that all the plasmon modes obtained by the resonant methods are predicted by the eigen-equation method. This effectively shows that the eigen-equation method is feasible and reliable in the process of finding plasmon modes. In this work, we generalize the eigen-equation method to the three-dimensional nanocubes. The effectiveness of the eigen method is further demonstrated, and various kinds of plasmons are displayed by charge distributions. The existence of the edge plasmons and the corner plasmons in nanocubes are further confirmed.