Two methods for the estimation of the interaction parameters in cubic equations of state by using the entire binary phase equilibrium database and the critical point locus, respectively, are presented. The solution of the optimization problem is accomplished in both methods by a Gauss-Newton-Marquardt minimization algorithm. The methods are computationally efficient and robust because they are based on implicit objective functions and hence avoid phase equilibrium or critical point calculations during the parameter optimization. The use of the entire phase equilibrium database and the critical locus can be a stringent test of the correlational ability of the equation of state. In the illustrative examples, the results were obtained by using the Peng-Robinson and the Trebble-Bishnoi equations of state with quadratic mixing rules and temperature-independent interaction parameters.