Learn German: Der Expressversand muss binnen eines Tages erfolgen. - The express shipping must occur within one day.

The temporal preposition binnen (within) can take either the genitive or the dative case. In this sentence, it triggers the genitive case, changing the masculine noun phrase ein Tag to eines Tages. Using the genitive with binnen is especially common in written or formal German.

Could I use the dative case with binnen in this sentence instead?

Yes, you could completely correctly say binnen einem Tag. While the genitive is preferred in formal writing (like official shipping terms), the dative is perfectly acceptable and is actually much more common in everyday spoken German.

How does binnen differ from innerhalb, which also means "within"?

They are virtually interchangeable when talking about time deadlines, so you could easily say innerhalb eines Tages here. The main difference is that binnen is exclusively temporal (used only for time), whereas innerhalb can be used for both time and physical space (like "inside" a building or area).

Why use erfolgen here instead of a more common word for "happen", like passieren?