Cancer spheroids are quasi-spherical structures originating from small clusters of cell aggregates seeded in vitro. They are often cultured within a hydrogel extracellular matrix (ECM) and are widely used to investigate tumor formation and evolution, including in the presence of pharmacological treatments. These culture models emulate essential properties of solid tumors and exhibit cell–cell and cell–ECM interactions. More interestingly, they can be cultured in microfluidic chips to better reproduce in vivo-like behavior. These biological systems help to understand tumor dynamics, drug penetration, and cellular behavior in a physiologically more relevant context than 2D cultures. In this work, we present a three-dimensional hybrid discrete-in-continuous model that captures key aspects of in vitro cancer spheroid formation and growth. Cells are described as discrete agents subject to mechanical forces such as adhesion and repulsion. Their dynamics are governed by systems of ordinary differential equations mimicking self-organization through typical terms of collective behavior and chemotaxis, while stochastic rules govern proliferation and differentiation events via Poisson processes. These cell-level dynamics are coupled to reaction-diffusion PDEs describing the evolution of chemical cues such as oxygen and growth factors. The model extends previous 2D frameworks by advancing to full 3D and improves computational performance using the PETSc library in C++ for parallel simulation. The implementation is designed to enrich the existing PhysiCell toolbox by incorporating a flexible and extendable description of intrinsic cell mechanics and phenotypes. The growth of spheroids is predicted through tailored simulation algorithms rooted in mathematical modeling. We validate our simulations against experimental data and conduct sensitivity analyses to examine correlations between parameters, spheroid diameter, and growth rate, which are then used for calibration. Lastly, we bridge the microscopic cell-based model with a macroscopic continuum description through a Kernel Density Estimation-inspired method, enabling a multiscale view of collective behavior in cancer spheroids with implications for biomedical applications.