Much remains unknown about the progression and heterogeneity of mutational processes in different cancers and their diagnostic and clinical potential. We develop methods and mathematical models to explore DNA context-dependent mutational patterns and underlying somatic cancer mutagenesis. We construct and analyze mutational profiles of cancer samples, that are categorized based on cancer type and primary tumor sites and are normalized by removing the bias from mutational hotspots with recurring mutations.We identify the combinations of underlying mutagenic processes including those related to infidelity of DNA replication and repair machinery, and various other endogenous and exogenous mutagenic factors. In addition, we derive mutagen or cancer-specific mutational background models and apply them to calculate expected DNA and protein site mutability to decouple relative contributions of mutagenesis and selection in carcinogenesis.