The cubic equation of state (CEoS) requires critical temperature (T-c), critical pressure (P-c), and the alpha (alpha) function for all components including polymers before it can be used for the prediction of phase behavior and thermodynamic properties for the system. For nonpolymers or conventional components, T-c, P-c, and alpha usually are available in databanks. However, this is not the case for polymers since their critical point is not measurable and they lack vapor pressures for the derivation of the a function. As a result, the task of finding CEoS critical constants as well as the alpha function for polymers becomes extremely challenging in the case of polymeric systems. A rigorous theory requiring only the liquid density data of the pure polymer is successfully developed in this work for the accurate prediction of the critical temperature, the critical pressure, and the alpha function for the pure polymer for use in all types of cubic equations of state. The proposed theory extends the application of cubic equations of state to polymer systems in a very simple fashion.