Taste it. Is it tender (as it would be if cooked) or crunchy (as if raw)? Though I cannot imagine eating raw beets, so I'd be surprised if they are raw. If they are raw or cooked but still firm, you could steam them for a few minutes to soften them up and make them tender.
They're probably raw for salads. If your beet cake is patterned on the carrot cake model, then the beets should probably be raw anyway. If you need to be able to puree them, though, do as above to test for crunch and proceed as cookbookchick recommends.
Taste them to make sure that they don't have any vinaigrette on them.
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