"She drinks a lot of juice."
Translation:Она пьёт много сока.
Partitive would be «соку», and yes, it can be used here too (but it’ll sound a bit old-fashioned and dialectal).
Russian has no real Partitive case, Genitive is usually used where other languages use Partitive. However, some nouns have a Partitive form (or the second genitive form, as we used to call it in the university).