Glioblastoma Multiforme (GBM), the most malignant human tumour, can be defined by the evolution of growing bio-nanomachine networks within an interplay between self-renewal (Grow) and invasion (Go) potential of mutually exclusive phenotypes of transmitter and receiver cells. Herein, we present a mathematical model for the growth of GBM tumour driven by molecule-mediated inter-cellular communication between two populations of evolutionary bio-nanomachines representing the Glioma Stem Cells (GSCs) and Glioma Cells (GCs). The contribution of each subpopulation to tumour growth is quantified by a voxel model representing the end to end inter-cellular communication models for GSCs and progressively evolving invasiveness levels of glioma cells within a network of diverse cell configurations. Mutual information, information propagation speed and the impact of cell numbers and phenotypes on the communication output and GBM growth are studied by using analysis from information theory. The numerical simulations show that the progression of GBM is directly related to higher mutual information and higher input information flow of molecules between the GSCs and GCs, resulting in an increased tumour growth rate. These fundamental findings contribute to deciphering the mechanisms of tumour growth and are expected to provide new knowledge towards the development of future bio-nanomachine-based therapeutic approaches for GBM.