Single-particle levels of unknown superheavy and extremely superheavy nuclei are studied using a modified Woods--Saxon potential, which are smooth functions of the number of nucleons. This extrapolation gives that neutron shell closure remains for N=308, and a proton shell has a gap at Z=164, which is weaker than that of a neutron shell. Seven unknown doubly magic spherical nuclei beyond 208Pb are found: 256U164, 298Fl184, 310184, 342Fl228, 366228, 462308, and 472308. Of these, the 298Fl184 and 472308 are beta-stable nuclei. The nucleus 472308 seems to be the heaviest nuclei based on the analysis of neutron and proton drip lines and the fissility line.