3D-printing technologies, such as biofabrication, capitalize on the homogeneous distribution and growth of cells inside biomaterial hydrogels, ultimately aiming to allow for cell differentiation, matrix remodeling, and functional tissue analogues. However, commonly, only the mechanical properties of the bioinks or matrix materials are assessed, while the detailed influence of cells on the resulting mechanical properties of hydrogels remains insufficiently understood. Here, we investigate the properties of hydrogels containing cells and spherical PAAm microgel beads through multi-modal complex mechanical analyses in the small- and large-strain regimes. We evaluate the individual contributions of different filler concentrations and a non-fibrous oxidized alginate-gelatin hydrogel matrix on the overall mechanical behavior in compression, tension, and shear. Through material modeling, we quantify parameters that describe the highly nonlinear mechanical response of soft composite materials. Our results show that the stiffness significantly drops for cell- and bead concentrations exceeding four million per milliliter hydrogel. In addition, hydrogels with high cell concentrations (≥6 mio ml-1) show more pronounced material nonlinearity for larger strains and faster stress relaxation. Our findings highlight cell concentration as a crucial parameter influencing the final hydrogel mechanics, with implications for microgel bead drug carrier-laden hydrogels, biofabrication, and tissue engineering.