Absorption spectra of very small metal clusters exhibit individual peaks that reflect the discreteness of their localized electronic states. With increasing size, these states develop into bands and the discrete absorption peaks give way to smooth spectra with, at most, a broad localized surface-plasmon resonance band. The widely accepted view over the last decades has been that clusters of more than a few dozen atoms are large enough to have necessarily smooth spectra. Here we show through theory and experiment that for the ubiquitous thiolate cluster compound Au 144 (SR) 60 this view has to be revised: clearly visible individual peaks pervade the full near-IR, VIS and near-UV ranges of low-temperature spectra, conveying information on quantum states in the cluster. The peaks develop well reproducibly with decreasing temperature, thereby highlighting the importance of temperature effects. Calculations using time-dependent density-functional theory indicate the contributions of different parts of the cluster-ligand compound to the spectra.