Resonance Raman spectra provide a valuable probe into molecular excited-state structures and properties. Moreover, resonance enhancement is of importance for the chemical contribution to surface-enhanced Raman scattering. In this work, we introduce a simplified sum-over-states scheme for computing Raman spectra and Raman excitation profiles. The proposed sum-over-states approach uses derivatives of electronic excitation energies and transition dipole moments, which can be efficiently computed from time-dependent density functional theory. We analyze and interpret the resonance Raman spectra and Raman excitation profiles of nucleic acid bases using the present approach. Contributions of individual excited states under strictly resonant and nonresonant conditions are investigated, and smooth interpolation between both limiting cases is obtained.