In microfluidic chips spheroids, spherical cell clusters, can be cultivated and formed in vitro from cells embedded in hydrogel extracellular matrices to reproduce realistic biological phenomena to investigate tumour formation and cell behaviour in a more physiological relevant context compared to traditional experiments in presence of drug treatment. The following work presents a three-dimensional extension of a mathematical discrete-in-continuous hybrid model for spheroid growth. A system of ordinary differential equations describe cell dynamics such as self-organizing collective interactions between cells as well as chemotactic effects, while stochastic biological processes like proliferation and differentiation are modeled through Poisson processes. This agent-based formulation is coupled with reaction–diffusion equations describing the evolution of chemical signals like oxygen and growth factors which allows the framework to replicate and also predict key features of in vitro cancer spheroid formation and growth. To address spheroid structures that deviate from spherical geometries, we incorporate adaptive clustering methods capable of identifying and tracking clusters with more general, ellipsoidal shapes. This enables a more flexible characterization of evolving spheroid morphologies. The model is furthermore highly customizable, allowing modifications of cell mechanical properties and interaction rules in order to reproduce different biological behaviours, such as lumen formation and coexistence of multiple cell types. The simulations are implemented in C++ using the PETSc library for efficient parallel computation and are intended to be integrated into the existing PhysiCell toolbox. The model parameters are calibrated using experimental data on spheroid diameter growth, and the framework is extended towards the macroscopic scale through a kernel density estimation inspired approach to describe larger cell populations in terms of density, providing insight into how biological and chemical factors shape collective cell behaviour during spheroid formation in the context of drug testing.