Why don't blue whales die from cancer in ridiculous numbers? The probability of one cell turning cancerous in a organism should surely be proportional to the number of cells in that organism.
Within species, we do see larger organisms are more likely to get cancer; taller humans have more deaths from cancer than shorter ones for example.
So we would expect blue whales to have much higher rates of cancer than humans, who in turn would have higher rates of cancer than mice. But we don't see the same relationship between size of the organism and cancer incidence when looking across species. This is Peto's Paradox.
We don't have a good explanation for this phenomenon yet, but it might not be too surprising in the end. It seems likely that there would be a selection pressure encouraging larger organisms to develop ways to suppress cancer better than smaller ones.