We have measured the volume and lattice parameters of Fe3C-cementite as a function of pressure to 73 GPa using synchrotron-based x-ray diffraction. Several samples were laser heated and temperature-quenched from >1,500 K while held at high-pressure. No pressure or temperature induced phase transitions are observed in this study, and the 300 K isothermal equation of state of Fe3C yields a best-fit bulk modulus, K0T, of 175±4 GPa and a of 5.2±0.3. The bulk sound speed of Fe3C under outer core conditions is calculated: barring higher pressure polymorphism or marked changes in compressibility on melting, carbon could produce some or all of the offset between seismic observations (PREM) and measurements on pure iron and iron-nickel alloys. Additionally, we model the thermodynamic stability of this phase at the conditions of Earth's mantle, and determine that in the presence of free iron (i.e. during core formation) the formation of Fe3C is strongly favored relative to carbonates.