Can you legally cash a check if someone gave you the money in cash to replace the check?

Yes. Bank tellers do this every day.

Answer and Clarification

No. There are many reason a person may decide to pay you in cash after they have written a check. They may find they don't have the funds in their checking to cover the check, they may have received some unexpected cash and would rather leave their money in the bank, you may have asked them for cash instead of the check. If you and the person who wrote the check had an understanding the cash was intended to replace the check for some reason then you cannot cash the check. Rather, you should return it or destroy it. Deliberately cashing a check that you know has been replaced with cash is stealing.

Updated Answer and ClarificationLegally, Yes. Should you? No.

The question did not ask whether it was moral and right to cash a check when one has received cash in its place. The question stated "Can you legally cash a check ..." and the answer remains yes. If the payor did not want the check cashed, s/he should have requested the check in return for the cash. Alternatively the payor may place a stop-payment on the check in an attempt to prevent the payee from "double-dipping." Under the UCC, unless the check is voided, it remains a valid promise to pay. If the payee receives both cash and the proceeds from the check, then the payor can sue in court. But, based on the question as stated above, absent any other information, the check may still be legally cashed.

Take a look at it another way. A gives a check to B, who signs over the check to C for services rendered. Before C goes to the Bank, A gives B cash to replace the check but doesn't get the check returned. That does not alter C's right to cash the check -- it's a valid promise to pay. [By the way, this is why merchants do NOT accept 3rd party checs!] A will have to take legal action against B for his/her "unjust enrichment" but it doesn't prevent the check from being legally cashed.