The energy density of nuclear system is derived based on the Skyrme forces and semi-empirical surface correption and Coulomb contribution. For the case of finite temperature, the analytical energy density, entropy density and free energy density are acquired with help of Sommerfield expansion to the Fermi-Dirac integrals. The energy, entropy, free energy per nucleon and the equation of state for hot nuclear matter and hot finite nuclei are calculated, compared and analysed. The possibility of studying dynamical evolution of hot nuclei is predicted.