Final answer:
Hepatitis B (HBV) and Hepatitis C (HCV) are the viruses that can establish a chronic liver infection leading to liver cancer. Hepatitis C is specifically known as an oncogenic virus with the ability to cause cancer.
Step-by-step explanation:
The viruses that can establish a chronic infection of the liver, which may progress to liver cancer, include Hepatitis B (HBV) and Hepatitis C (HCV). Both HBV and HCV can cause chronic hepatitis, which is a long-term liver infection. This chronic state can potentially lead to further liver damage, cirrhosis, and ultimately, liver cancer. Hepatitis C, in particular, is known for causing low-level liver damage that often goes unnoticed, making it more likely for the chronic infection to persist for years. Furthermore, Hepatitis C is categorized as an oncogenic virus, which means it has the potential to cause cancer by interfering with the normal regulation of the host cell cycle.