Prediction of cohesive energy of crystals is of particular interest in order to understand crystal growth mechanisms for further molecular engineering. In this study, we have aimed at assessing the accuracy of dispersion-corrected calculations (DFT-D2, DFT-D3, and DFT-NL) in reproducing the experimental cohesive energy of the anthracene crystal. Preliminary comparison of the interaction energies calculated at revPBE(0)-D3 and revPBE(0)-NL levels in isolated dimers (taken from the crystalline structure) with benchmark calculations performed at the SCS-MP2 and LPNO-pCCSD1a level enlightens the reliability of these DFT-based methods for which the best accuracy achieved is within 1-2 kJ/mol of the ab initio methods. Interestingly, the evaluation of the cohesive energy reveals that 35-37 of this energy come from the consideration of a second coordination shell. Three-body interaction energy correction is calculated for revPBE-D3 functional and happens to reduce the cohesive energy of an anthracene nanoaggregate by 7 kJ/mol, while similar results are obtained with revPBE(0)-NL functional. In the end, dispersion-corrected estimates of the cohesive energy show sufficiently good agreement with experiment.