On the Bundestag building, the inscription reads "dem deutschen Volke", the German people. It is in the dative case. Why is the nominative case "das deutsches Volk" not used?
For the same reason you use to in an English dedication:
To my father
You wouldn't just put 'My father', since you're telling us who you are dedicating the book to, not what it is.
It's an ellipsis of
„Dieses Parlament ist dem deutschen Volk gewidmet“ (This parliament is dedicated to the German people).
Widmen requires a dativ object in German.
See here for a detailed article about this inscription (unfortunately in German only).
Similar typical inscriptions are "Dem Gedenken an ...", "Den Opfern von ..." usw.
This is what's called a dativus finalis
It tends to denote purpose and thus means "this is for [the benefit of] the German people".
Latin knew the same notion, an example would be "tibi laetitiae", meaning something along the lines of "for your enjoyment".
A simple nominative wouldn't transport this meaning (rather, it wouldn't transport much meaning on a building).
it's the same dative case as:
to whom it may concern ...