I've been struggling to find an accurate expression that translates to Spanish the word "whatsoever".
I think it depends on the context. In many contexts, whatsoever adds emphasis to any. "I don't really care for any style of architecture whatsoever."
In that context, I would use "cualquiera" or "cualesquiera" as translating both the "any" and the "whatsoever".
But you have to be careful. In a lot of phrases, these two words carry an overtone of mediocrity. That might not be what you are trying to express.
As Walter says, it depends on the context, and it's mostly an issue of emphasis. Some examples:
(last one added as per tchrist's comment)