Relativistic Breit-Pauli R-Matrix calculations of the photoionization cross sections in the energy region of the 2p inner-shell of free Mg and Mg confined in a C₆₀ molecule have been performed. For the free case, Mg⁺ orbitals are generated using Hartree-Fock (HF) and multiconfiguration HF (MCHF) programs. Multiconfiguration wavefunctions of confined Mg for the final states of ion core (target states) were obtained using modified MCHF and HF codes. The C₆₀ confinement potential is modeled as an attractive spherical potential of inner radius 5.8 a.u, thickness of 1.89 a.u. and a depth U₀ of 0.302 a.u. Based on the photoionization cross section calculation, an eigenphase derivative technique, the QB method, along with the quantum defect theory were employed to obtain the resonance positions and effective quantum numbers (quantum defects) of the lower members of various autoionizing series over the 54 eV to 65 eV photon energy range. The calculations were performed for a variety of well depths up to 0.302 a.u. in order to study the evolution of photoionization cross section from free Mg to Mg@C₆₀. The ionization energy of the inner and outer shells of the Mg ground state increase with as the well depth is increasing. Moreover, the photoionization cross section of Mg in the vicinity of the 2p thresholds, which is dominated in the threshold region by core-excited and doubly-excited nln^’l^’ resonances, changes dramatically in the presence of the confining well. A complex pattern of changes occur with increasing well depth, with some of the resonances moving to lower energy and some to higher. Reasonably good agreement is obtained between this calculation and few available NIST values for the free Mg case.