Results of cold and hot symmetric nuclear matter and pure neutron matter calculations are presented. The Brueckner-Hartree-Fock (BHF) approximation + two body density dependent Skyrme potential which is equivalent to three body interaction are used. Various modern nucleon-nucleon (NN) potentials are used in the framework of BHF approxima-tion, e.g.: CD-Bonn potential, Nijm1 potential, Reid 93 potential and Argonne V18 potential. The bulk properties of asym-metric nuclear matter are computed such as the equation of state (EOS) at (T = 0), pressure at (T = 0, 5 and 10 MeV), single particle potential, free energy at (T = 5 and 10 MeV), nuclear matter incompressibility and the symmetry energy. Also the bulk properties of pure neutron matter are computed such as the EOS at (T = 0), pressure at (T = 0, 3 and 6 MeV), single particle potential, free energy at (T = 3 and 6MeV). Good agreement is obtained in comparison with previous theoretical estimates and experimental data.