It is worth to follow Amos' link. Especially the part when it comes to explanations was interesting for me.
Of course it depends completely on the definition of 'culture' whether whales have it or not. In the bad old times, even several subgroups of humans didn't have culture according to a very europeocentric definition. Ants, for instance, have social behaviour according to one definition but not according to another.
Learning of the type described in the article above has been shown in several species of birds and of mammals, it would be a wonder if it did not occur in whales.

What intrigues me most is that this behaviour has so far to the best of my knowledge only be demonstrated in animals that can dream, i.e. that have REM-sleep. And there are a lot of interesting speculations about the function of dream for learning and storing new behaviors. I see a speculative connection there which I have not seen in print yet. But I doubt that I am the only one who sees it. A scientific sensation for me would be the demonstration of culture in the above sense in a species without REM-sleep. This would be a finding which would necessitate a major rethinking about learning and storage.

Wolfgang