"I know when the party is."
Translation:Yo sé cuándo es la fiesta.
It's not about it being necessary or not. It's about whether it has to be accented or it has to be unaccented. The accented
cuándo is used for questions. Otherwise, non-accented
cuando is used.
¿Cuándo empiezas a trabajar? (When do you start working?)
Voy a empezar a trabajar cuando termine de estudiar. (I will start working when I finish studying.)
Unfortunately, that rule is an oversimplification. The use here is close to asking a question; it's saying that I know the answer to the question. It's not introducing an adverbial clause.
Compare ‘Yo lo sé cuando la fiesta es.’; that's a little weird and required a couple of other adjustments to be grammatically correct, but it means that the time when I don't know some thing is at the same time as the party.