Despite their potential to address crucial bottlenecks in computing architectures and contribute to the pool of biological inspiration for engineering, pathological biological mechanisms remain absent from computational theory. We hereby introduce the concept of cancer-inspired computing as a paradigm drawing from the adaptive, resilient, and evolutionary strategies of cancer, for designing computational systems capable of thriving in dynamic, adversarial or resource-constrained environments. Unlike known bioinspired approaches (e.g., evolutionary and neuromorphic architectures), cancer-inspired computing looks at emulating the uniqueness of cancer cells survival tactics, such as somatic mutation, metastasis, angiogenesis and immune evasion, as parallels to desirable features in computing architectures, for example decentralized propagation and resource optimization, to impact areas like fault tolerance and cybersecurity. While the chaotic growth of cancer is currently viewed as uncontrollable in biology, randomness-based algorithms are already being successfully demonstrated in enhancing the capabilities of other computing architectures, for example chaos computing integration. This vision focuses on the concepts of multilevel intelligence and context-driven mutation, and their potential to simultaneously overcome plasticity-limited neuromorphic approaches and the randomness of chaotic approaches. The introduction of this concept aims to generate interdisciplinary discussion to explore the potential of cancer-inspired mechanisms toward powerful and resilient artificial systems.