The packing arrangement of organic π-conjugated molecules in a nanoscale material can have a strong impact on their optical properties. Here, using real-time-propagation time dependent density functional theory (rt-TDDFT) calculations with the support of transition contribution maps, we study how modifications in the packing arrangement (cubic-like and chain-like aggregates composed of eight C60 molecules) and packing density (assembled at close distances with center-to-center inter-fullerene distances (d) varying from 9 Å to 11 Å) of C60 molecules affect the optical properties of cluster aggregates. The important conclusions drawn from this work are summarized as follows. For d = 9 Å, the charge transfer excitons produced by cubic and chain-like C60 cluster aggregates have highly different optical characteristics, as evidenced by the transition contribution maps. On the other hand, for d = 10 Å and 11 Å, both kinds of aggregates produce qualitatively similar optical features with the emergence of Wannier-like delocalized excitons having distinct degrees of localization and spatial distribution. The theoretical findings in this study elucidate the optical excitations in C60 cluster aggregates and could help in the design of more efficient organic devices.