The recent resumption of the synthesis of new superheavy nuclei has provided relevant results for nuclear physics and chemistry. These nuclei provide experimental confirmation of theoretical calculations that predict the existence of two islands of stability, one with maximum stability in Z=114 and N=184 and the other in Z=120 or Z=126 and N=184 or N=228. Through cold fusion, recently synthesized nuclei with Z=114, 116 and 118 have confirmed the theoretical predictions, providing a possibility of reaching the maximum of these islands of stability. Because of the low production rate and the extremely short half-life of these nuclei, it has not yet been possible to determine their energy spectra. However, it has been theoretically predicted that the nuclei should acquire a spherical form in these islands of stability, thus supplying characteristic vibrational energy spectra. The predictions also indicate the existence of deformed superheavy nuclei in the region between the islands, which can possess rotational energy spectra. In this work, the hydrodynamic equation of energy was corrected by inserting terms referring to coulombian effects, shell closure and nuclear deformation, enabling us to predict the energies of the first excited state for superheavy nuclei of quadrupole deformation, the quadrupole phonon state and an octupole phonon for spherical superheavy nuclei. Four anharmonic vibrational models were then used to describe higher energy states of the nuclei in question. The energy spectra of the (266)104, (268)106, (270)108, (274)110, (278)112, (298)114, (304)120, (348)120, (354)126 nuclei and their closest neighbors were determined.
