We present the results of the analysis of eight years of Fermi-LAT data of the pulsar/pulsar wind nebula complex PSR J0205+6449/3C 58. Using a contemporaneous ephemeris, we carried out a detailed analysis of PSR J0205+6449 both during its off-peak and on-peak phase intervals. 3C 58 is significantly detected during the off-peak phase interval. We show that the spectral energy distribution at high energies is the same disregarding the phases considered, and thus that this part of the spectrum is most likely dominated by the nebula radiation. We present results of theoretical models of the nebula and the magnetospheric emission that confirm this interpretation. Possible high-energy flares from 3C 58 were searched for, but none were unambiguously identified.