The prepositional object 'whom' is required in formal English.
The first sentence, 'To whom did you give the parcel?" would satisfy the requirements of even the strictest grammarians, i.e., those who believe that whenever possible a sentence should not end with a preposition. In formal written English this is probably the preferred way of expressing the idea.
The second sentence 'Whom did you give the parcel to?' is also correct. Most grammar experts believe that ending a sentence with a preposition in a sentence like this is fine when you are speaking because it sounds more natural. I am sure, however, that you can find someone who disagrees.
In informal spoken English the sentence 'Who did you give the parcel to?' is perfectly acceptable.
I didn't see that fdmaxey had already answered your question before I posted this. I agree with his assessment.