The pressure evolution of phase stability, structural and mechanical properties of Fe₃C in ferro-magnetic (FM) and high pressure non magnetic (NM) phase is investigated from first principle calculations. The 2^nd order FM to NM phase transition of Fe₃C is identified around 60 GPa. Pressure (or density) variation of sound velocities from our ab-initio calculated single crystal elastic constants are determined to predict these parameters at Earth's outer core pressure.