Mathematical models have become increasingly more accurate in terms of the description of cancer growth in both space and time. However, the limited amount of data typically available has resulted in a larger number of qualitative rather than quantitative studies. In the present study, we provide an integrated experimental-computational framework for the quantification of the morphological characteristics and the mechanistic modelling of cancer progression in 3D environments. The proposed framework allows for the calibration of multiscale-spatiotemporal models of cancer growth using state-of-the-art 3D cell culture data, and their validation based on the resulting experimental morphological patterns. The implementation of it enables us to pursue two goals; first, the quantitative description of the morphology of cancer progression in 3D cultures, and second, the relation of tumour morphology with underlying biophysical mechanisms that govern cancer growth. We apply this framework to the study of the spatiotemporal progression of Triple Negative Breast Cancer cells cultured in Matrigel scaffolds, and validate the hypothesis of chemotactic migration using a multiscale Keller-Segel model. The results reveal transient, nonrandom spatial distributions of cancer cells that consist of clustered, and dispersion patterns. The proposed model was able to describe the general characteristics of the experimental observations and suggests that cancer cells exhibited chemotactic migration and accumulation, as well as random motion throughout the period of development. To our knowledge, this is the first time that a multiscale model is used to quantify the relationship between the spatial patterns and the underlying mechanisms of cancer growth in 3D environments.