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Semiconducting nanoparticles are the building blocks of optical nanodevices as their electronic states, and therefore light absorption and emission, can be controlled by modifying their size and shape. CdSe is perhaps the most studied of these nanoparticles, due to the efficiency of its synthesis, the high quality of the resulting samples, and the fact that the optical gap is in the visible range. In this article, we study light absorption of CdSe nanostructures with sizes up to 1.5nm within density functional theory. We study both bulk fragments with wurtzite symmetry and fullerene-like core-cage structures. The comparison with recent experimental optical spectra allows us to confirm the synthesis of these fullerene-like CdSe clusters.