From IMDb's soundtrack search:

Animated short "Der Fuehrer's Face" (1942) 'A marching band of Germans, Italians, and Japanese march through the streets of swastika-motif Nutziland, serenading "Der Fuehrer's Face." Donald Duck, not living in the region by choice, struggles to make do with disgusting Nazi food rations and then with his day of toil at a Nazi artillery factory. After a nervous breakdown, Donald awakens to find that his experience was in fact a nightmare.'

Song "Der Fuehrer's Face" by Oliver Wallace, who composed a lot of stuff for Disney.
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The song also appears in the film "Meet the People" (1944), where it is performed by Spike Jones and His City Slickers, and in the Bruce Willis film "Hart's War" (2002) - no performer given.