Entschuldigung (noun, capital E!) is used for "I'm sorry" and "excuse me", but you cannot literally translate "being sorry for someone's loss" and use "Entschuldigung" here. It makes no sense in German. Instead, you'd use "Herzliches Beileid" (official, a bit formal) or "das tut mir leid für dich" (informal, not if someone passes away, but ok when someone fails a test.

Entschuldigung (noun, capital E!) is used for I’m sorry and excuse me, but you cannot literally translate being sorry for someone’s loss and use Entschuldigung here. It makes no sense in German. Instead, you’d use

Herzliches Beileid (official, a bit formal)

or

Das tut mir leid für dich (informal, not if someone passes away, but ok when someone fails a test.)