"No, I am your father!"
Translation:Nem, én vagyok az apád!
In my experience, apuka and anyuka are very diminutive, borderline "cutesy" words. You're most likely to use them if you are a child or if you're speaking to a child (Hol van az apukád?) You probably wouldn't use them seriously when talking to another adult.
Édesanya and édesapa are also somewhat "sweet" terms but they don't have the same childish-cutesy sound - they just soften the somewhat formal edge of plain apa and anya.
"dad" for édesapa doesn't sound quite right to me. To me, it's not really as casual as that. It's more as if you could say "Your dear father" or "your dear old dad" without it sounding quite so overwrought as those phrases do.
Perhaps native speakers will explain the connotations more accurately.
"Édesapa" and "édesanya" are more formal than "apa" and "anya", if only because they are longer words.
Daddy - Dad - Father >> Apu - Apa - Édesapa
And "apád", "anyád" can be a little rough, especially when used with some not so pleasant words...
But there is not one correct answer here. "Ahány ház, annyi szokás." Every family is different. Whatever our parents taught us to call them, that will be "the norm" for us, and what other families do will be a bit unusual to us. One person's "father" is another's "daddy". And "apuka" could be cutesy to one person, and totally formal to another. Because these words will frequently lose their literal meanings and become quasi names for those people.
Köszi a hozzászólást! :D
I'm trying to say thanks for the input/comment. This is another word I've never used, so I might have chosen the wrong one. The online dictionary I use lists several words along with examples, and after reading the examples for context and to see which is most commonly used, I then choose which word to use. It seems that so far I've done well, but that might not always be the case. ;)