Learn German: Wir befestigen das Bild mit Klebeband statt eines Nagels. - We are attaching the picture with tape instead of a nail.

The preposition statt (instead of) forces the following noun phrase into the genitive case. For masculine nouns like der Nagel (the nail), the genitive rule adds an -s or -es to the end of the noun, and the indefinite article changes to eines.

Could I say anstatt eines Nagels in this sentence instead?

Yes, absolutely! Statt and anstatt are completely interchangeable. They both mean "instead of" and both require the genitive case. Statt is simply a shorter version that is very common in everyday use.

The preposition mit takes the dative case. Why is there no dative article in front of Klebeband?

Just like in English ("with tape"), Klebeband is used here as an uncountable material or mass noun. Because we aren't saying "with a tape" or "with the tape", no article is needed. If you specifically meant "with the tape", you would use the dative article: mit dem Klebeband.

Will I ever hear statt einem Nagel using the dative case instead?

Yes. In casual, spoken German, native speakers frequently substitute the dative case for the genitive after statt. However, standard written German—and your B1 language exams!—require the proper genitive case shown in this sentence: statt eines Nagels.