Periodic superstructures of plasmonic nanoparticles have attracted significant interest because they can support coupled plasmonic modes, making them interesting for plasmonic lasing, metamaterials, and as light-management structures in thin-film optoelectronic devices. We have recently shown that noble metal hydrogel core-shell colloids allow for the fabrication of highly ordered 2-dimensional plasmonic lattices that show surface lattice resonances as the result of plasmonic/diffractive coupling (Volk, K.; Fitzgerald, J. P. S.; Ruckdeschel, P.; Retsch, M.; Konig, T. A. F.; Karg, M. Reversible Tuning of Visible Wavelength Surface Lattice Resonances in Self-Assembled Hybrid Monolayers. Adv. Optical Mater. 2017, 5, 1600971, DOI: 10.1002/adom.201600971). In the present work, we study the photonic properties and structure of 3-dimensional crystalline superstructures of gold hydrogel core-shell colloids and their pitted counterparts without gold cores. We use far-field extinction spectroscopy to investigate the optical response of these superstructures. Narrow Bragg peaks are measured, independently of the presence or absence of the gold cores. All crystals show a significant reduction in low-wavelength scattering. This leads to a significant enhancement of the plasmonic properties of the samples prepared from gold-nanoparticle-containing core-shell colloids. Plasmonic/diffractive coupling is not evident, which we mostly attribute to the relatively small size of the gold cores limiting the effective coupling strength. Small-angle neutron scattering is applied to study the crystal structure. Bragg peaks of several orders clearly assignable to an fcc arrangement of the particles are observed for all crystalline samples in a broad range of volume fractions. Our results indicate that the nanocrystal cores do not influence the overall crystallization behavior or the crystal structure. These are important prerequisites for future studies on photonic materials built from core-shell particles, in particular, the development of new photonic materials from plasmonic nanocrystals.