I've been struggling to find an accurate expression that translates to Spanish the word "whatsoever".
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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)
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.