The first case in your examples uses the pronoun attributively, i.e. it inflects like an adjective. That means that you have no choice: it has to be "beide Getränke", because that's what the inflection rules say.

The second case uses substituting pronouns. You can use "beides" because that's the most general form, which can substitute for everything, whether masculine, feminine or neuter. But you can also parse it as a (very common) elliptical construction: "beide" is understood as short for "beide (Getränke)" if that term was used previously, and that's why "beide" is also correct in the second case.