Application of artificial intelligence (AI) in precision oncology typically involves predicting whether the cancer cells of a patient (previously unseen by AI models) will respond to any of a set of existing anticancer drugs, based on responses of previous training cell samples to those drugs. To expand the repertoire of anticancer drugs, AI has also been used to repurpose drugs that have not been tested in an anticancer setting, i.e., predicting the anticancer effects of a new drug on previously unseen cancer cells de novo. Here, we report a computational model that addresses both of the above tasks in a unified AI framework. Our model, referred to as deep learning-based graph regularized matrix factorization (DeepGRMF), integrates neural networks, graph models, and matrix-factorization techniques to utilize diverse information from drug chemical structures, their impact on cellular signaling systems, and cancer cell cellular states to predict cell response to drugs. DeepGRMF learns embeddings of drugs so that drugs sharing similar structures and mechanisms of action (MOAs) are closely related in the embedding space. Similarly, DeepGRMF also learns representation embeddings of cells such that cells sharing similar cellular states and drug responses are closely related. Evaluation of DeepGRMF and competing models on Genomics of Drug Sensitivity in Cancer (GDSC) and Cancer Cell Line Encyclopedia (CCLE) datasets show its superiority in prediction performance. Finally, we show that the model is capable of predicting effectiveness of a chemotherapy regimen on patient outcomes for the lung cancer patients in The Cancer Genome Atlas (TCGA) dataset.