This is a good question. It is also the excellent title of a rather speculative paper. The point is that cancer is a disease that results from us, and whales, being multicellular animals. We are made from around a few hundred trillion cells. If one of them starts dividing uncontrollably then it can produce more and more cells. This is a tumour, and if unchecked can kill us. But a blue whale is a around 1000 times bigger than we are, so has 1000 times more cells, so naively should 1000 times more likely to get cancer.
As cancer kills about 1/3 of us, then if blue whales were much more likely to get cancer than us, they they’d all be dead of cancer. But they are not.
I am reading up on the statistics of cancer at the moment, as it is a many step random process, like the nucleation of crystals, which I’m studying. There is an interesting paper by Caulin and Maley with ideas of not only why whales do not suffer from cancer more than we do (they do die of cancer, it just appears to be no more common than in us), but why mice, which are much smaller than we are, do die of cancer.
Basically, it is probably true that as larger animals evolved they evolved more and better defence mechanisms against cancer, to cope with the increased risk due to the increased number of cells. For example there are so-called tumour-suppressor genes that tend to put the brakes on cells multiplying. There is some evidence that elephants have more of these than we do.
But size is not everything, at top-left is a picture of not only arguably the ugliest mammal of all, but also the longest-lived rodent. It is the naked mole-rat, a weird and very long lived rodent. It holds the record for the longest-lived rodent at 28 years. This is about 10 times the typical lifespan of a rat. Despite this, cancer appears to be very rare in the naked mole rat. We don’t know why, but it would be good to know, it might tell us something important about this disease.