We report on the direct observation of collective electronic properties in assembled CdS quantum particles (QPs) arranged in periodic layers. Within each layer the QPs are of the same average size, either 2.5 or 5 nm, and the layers are arranged in a cascade-like pattern. The electronic properties of the QPs were studied using a new method, the attenuated low energy photoelectron spectroscopy (A-LEPS), in which a "pump" laser excites the QPs and a "probe" laser ejects photoelectrons from the QPs and from the metal substrate. The A-LEPS method provides information about the populated electronic states of the QPs (including the splitting between the light/heavy hole and split-off bands) and how these states depend on the interparticle interactions.