The calculation of the isobaric heat capacities of the liquid and solid phase of molecules at 298.15 K is presented, applying a universal computer algorithm based on the atom-groups additivity method, using refined atom groups. The atom groups are defined as the molecules' constituting atoms and their immediate neighbourhood. In addition, the hydroxy group of alcohols are further subdivided to take account of the different intermolecular interactions of primary, secondary and tertiary alcohols. The evaluation of the groups' contributions has been carried out by means of a fast Gauss-Seidel fitting calculus using experimental data from literature. Plausibility has been tested immediately after each fitting calculation using a 10-fold cross-validation procedure. For the heat capacity of liquids, the respective goodness of fit of the direct (R2) and the cross-validation calculations (Q2) of 0.998 and 0.9975, and the respective standard deviations of 8.2 and 9.16 J/mol/K, together with a medium absolute percentage deviation (MAPD) of 2.69%, based on the experimental data of 1133 compounds, proves the excellent predictive applicability of the present method. The statistical values for the heat capacity of solids are only slightly inferior: for R2 and Q2, the respective values are 0.9915 and 0.9875, the respective standard deviations are 12.19 and 14.13 J/mol/K and the MAPD is 4.65%, based on 732 solids. The predicted heat capacities for a series of liquid and solid compounds has been directly compared to those received by a complementary method based on the "true" molecular volume [1] and their deviations elucidated.