A method of calculating nonlinear terms in free energy is studied for the density functional theory of a molecular system with orientational freedoms. In the method, a free energy functional is expanded into Taylor series of density fields, and then the coefficients are calculated from the cumulant expansion. Using the method, expansion coefficients of third and forth orders are explicitly derived by the three-point and four-point coefficients of the cumulant expansion. For the third-order coefficient, two approximations are compared by calculations of the triplet direct correlation function. The approximation obtained by expansion in terms of pair correlation functions gives abrupt changes in the triplet direct correlation function. The simplified Kirkwood superposition approximation gives slow changes in the function, though its value should be scaled down by a small parameter.