[idontknowmuch]

Viruses are just another "mutagen". No different from UV causing DNA damage in your skin cells, other than the mechanism in which it occurs. The cause for cancer is well-known and, in hindisght, obvious, which is mutation.

The challenge though is mutations can happen in a plethora of ways and their effect is highly dependent on which gene is mutated. There is also the tissue context, e.g. inflammation, spatial structure, etc., that can setup a background for increased mutation. That is why targeted therapies are often the most effective, because they target the general causative feature of a given tumour subtype, the problem is not every protein can be targeted now and each tumour, even within the same subtype has their own unique mutational profile due to the stochasticity of the way mutations occur over repeated rounds of cell division.

And back to viruses, yes they cause cancer because they can mutate DNA. But it's pretty clear, most of the viral "enriched" cancer types are generally in places where transmission is commonplace, e.g. reproductive organs or head/neck.