Brain development involves precisely orchestrated genetic, biochemical, and mechanical events. At the cellular level, neuronal proliferation in the innermost zone of the brain followed by migration towards the outermost layer results in a rapid increase in brain surface area, outpacing the volumetric growth of the brain, and forming the highly folded cortex. This work aims to provide mechanistic insights into the process of brain development and cortical folding using a biomechanical model that couples cell division and migration with volumetric growth. Unlike phenomenological growth models, our model tracks the spatio-temporal development of cohorts of neurons born at different times, with each cohort modeled separately as an advection-diffusion process and the total cell density determining the extent of volume growth. We numerically implement our model in Abaqus/Standard (2020) by writing user-defined element (UEL) subroutines. For model calibration, we apply in utero electroporation (IUE) to ferret brains to visualize and track cohorts of neurons born at different stages of embryonic development. Our calibrated simulations of cortical folding align qualitatively with the ferret experiments. We have made our experimental data and finite-element implementation available online to offer other researchers a modeling platform for future study of neurological disorders associated with atypical neurodevelopment and cortical malformations.