English Translation
Do you want another one of these?
Why is it “noch eines davon” here and not just “noch ein davon”?
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You cannot use “ein” without a noun.
Compare:
Do you want another piece of these? = Willst du noch ein Stück davon?
Do you want another one of these? "Willst du noch ein(e)s davon?
Today, you will hear and often read “eins” instead of “eines”.
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Ah, thank you. I’ve heard “noch eins” before in conversation but had never noticed the pattern there regarding using it with/without a noun. Good to know.
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Could it also be in the masculine or feminine case? For example:
Willst du noch einen (Teil) davon?
How do we know it is in neutral without context?
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Hello and welcome!
You are right. You cannot know without context.
Two persons drinking Schnaps.
“Willst du noch einen?” (because of “der Schnaps”)
Two persons drinking Beer.
“Willst du noch eins?” (because of “das Bier”)
Two persons drinking punch.
“Willst du noch eine?” (because of “die Bowle”)
Prost! 
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