The water octamer, with its cubic structure consisting of six four-membered rings, presents an excellent system in which to unravel the cooperative interactions driven by subtle changes in the hydrogen-bonding topology. Although many distinct structures are calculated to exist, it has not been possible to extract the structural information encoded in their vibrational spectra because this requires size-selectivity of the neutral clusters with sufficient resolution to identify the contributions of the different isomeric forms. Here we report the size-specific infrared spectra of the isolated cold, neutral water octamer using a scheme based on threshold photoionization using a tunable vacuum ultraviolet free electron laser. A plethora of sharp vibrational bands features are observed for the first time. Theoretical analysis of these patterns reveals the coexistence of five cubic isomers, including two with chirality. The relative energies of these structures are found to reflect topology-dependent, delocalized multi-center hydrogen-bonding interactions. These results demonstrate that even with a common structural motif, the degree of cooperativity among the hydrogen-bonding network creates a hierarchy of distinct species. The implications of these results on possible metastable forms of ice are considered.