Cancer development and progression result from somatic evolution by an accumulation of genomic alterations. The effects of those alterations on the fitness of somatic cells lead to evolutionary adaptations such as increased cell proliferation, angiogenesis, and altered anticancer drug responses. However, there are few general mathematical models to quantitatively examine how perturbations of a single gene shape subsequent evolution of the cancer genome. In this study, we proposed the gene gravity model to study the evolution of cancer genomes by incorporating the genome-wide transcription and somatic mutation profiles of ~3,000 tumors across 9 cancer types from The Cancer Genome Atlas into a broad gene network. We found that somatic mutations of a cancer driver gene may drive cancer genome evolution by inducing mutations in other genes. This functional consequence is often generated by the combined effect of genetic and epigenetic (e.g., chromatin regulation) alterations. By quantifying cancer genome evolution using the gene gravity model, we identified six putative cancer genes (AHNAK, COL11A1, DDX3X, FAT4, STAG2, and SYNE1). The tumor genomes harboring the nonsynonymous somatic mutations in these genes had a higher mutation density at the genome level compared to the wild-type groups. Furthermore, we provided statistical evidence that hypermutation of cancer driver genes on inactive X chromosomes is a general feature in female cancer genomes. In summary, this study sheds light on the functional consequences and evolutionary characteristics of somatic mutations during tumorigenesis by propelling adaptive cancer genome evolution, which would provide new perspectives for cancer research and therapeutics. 