The core electron binding energies (CEBE's) of benzene, seven monosubstituted benzenes (Ph-X) and one disubstituted benzene (p-NH2-C6H4-NO2) were calculated using density-functional theory (DFT). The unrestricted generalized transition-state (uGTS) model was employed. The DeMon DFT program with a combined functional of Becke's exchange (B88) with Perdew's correlation (P86) was used. The average absolute deviation of the calculated CEBE's of the title compounds was 0.3 eV when the cc-pVDZ basis set was used. The "CEBE shift" of the ring carbon in Ph-X was calculated while taking the CEBE on the ring carbon in Ph-H as a reference. The thus-calculated CEBE shifts agree with experiment within the value of the average absolute deviation, 0.1 eV. The signs and quantitative numerical values of the CEBE shifts are very close to the corresponding Hammett sigma constants.731124532460