In the present study, the electronic structure of neutral He and Li atoms confined at the center of an impenetrable spherical cavity of varying radius has been investigated. Average, state, orbital energies and wave functions for the ground and excited state electron configurations 1snl (1s2nl)[n = 2, 3, 4 and l = 0, 1, 2 and 3] have been calculated using the method that is a combination of quantum genetic algorithm procedure and Hartree-Fock Roothaan. The atomic orbitals built up from Slater-type orbitals are used in calculations. The average state and orbital energies have been calculated for the first time for the higher excited states with nl [n = 3,4 and l = 1,2,3 for confined He atom and n = 3,4 and l = 0, 1,2,3 for confined Li atom]. The results show that impurity charge and spatial confinement have a great impact on orbital energies, average, state energies and virial coefficients of the system, especially in strong confinement region. In addition, it is seen that when cavity radius is extremely large, all state energies and virial coefficients approach the corresponding values of free atom.