The new era of artificial intelligence demands large-scale ultrafast hardware for machine learning. Optical artificial neural networks process classical and quantum information at the speed of light, and are compatible with silicon technology, but lack scalability and need expensive manufacturing of many computational layers. New paradigms, as reservoir computing and the extreme learning machine, suggest that disordered and biological materials may realize artificial neural networks with thousands of computational nodes trained only at the input and at the readout. Here we employ biological complex systems, i.e., living three-dimensional tumour brain models, and demonstrate a random neural network (RNN) trained to detect tumour morphodynamics via image transmission. The RNN, with the tumour spheroid as a three-dimensional deep computational reservoir, performs programmed optical functions and detects cancer morphodynamics from laser-induced hyperthermia inaccessible by optical imaging. Moreover, the RNN quantifies the effect of chemotherapy inhibiting tumour growth. We realize a non-invasive smart probe for cytotoxicity assay, which is at least one order of magnitude more sensitive with respect to conventional imaging. Our random and hybrid photonic/living system is a novel artificial machine for computing and for the real-time investigation of tumour dynamics.