It would be both: 'I like cake with milk' and 'I like the cake with milk.'
Actually accusative is always used unless the object is indefinite (a/an, some, any)
Here, the object is neither definite nor indefinite. It's a general thing. So you should use accusative here. Well, yes the sentence itself didn't use accusative, it's related to the verb sevmek. With sevmek, you are free to use accusative or not.
"Sütlü pasta seviyorum." and "Sütlü pastayı seviyorum."
Is it possible to decide here if you like a cake with a glass of milk, or if you like the cake made with milk.
The second sentence (with the accusative) specifies the cake, so would this be closer to the second meaning?
No, we distinguish those two meanings by using different endings
Sütlü -> with milk / au lait (including milk)
Sütle -> with milk / avec le lait (together with milk)
Sütlü pasta seviyorum. or Pastayı sütlü seviyorum. -> I like cake (made) with milk.
Pastayı sütle seviyorum. -> I like cake with (a glass of) milk.
Yes exactly. Let me make some clarifications though.
For the instrumental case you can also use its postposition version ile instead of -le/-la. e.g. süt ile = sütle
We actually don't consider -li/lı/lu/lü to be a case, rather we consider it to be a suffix to form adjectives from nouns e.g. milk (süt) - milky (sütlü)
(For some reason I cannot reply to your message directly)
Ah, thank you very much. I just now realized there is a difference: The Instrumental case ending uses the SMALL vowel harmony. Which is in a way very logical, as it seems that it is used for all cases describing locations in some way (where, to where, from where and now "besides where").
Or better, to make it clear what I mean: German has only four cases, and the Turkish cases using the small vowel harmony happen to be the ones you would build by using a proposition (some merged with the article) + the dative case in German.
1) general direct boject always come direct before the verb in Turkish, so we know that "pasta" is the direct object
2) "Sütlü" is an adjective meaning "containing milk/with milk." You can't really love adjectives in Turkish or English (unless they are acting like nouns, which it is not in this sentence)
This is not an actual "cake with milk". It is not a cake with a glass of milk. Instead, it is a cake made USING milk. "Sütlü" literally means "milky", that is, containing milk. Similarly to how you can say "sugary", "spicy", "salty" in English.
An actual "with milk" situation would be "sütLE" or "süt ile". That is what corresponds to your "adamla" / "adam ile". The "with" ending uses only a two-way matching: it is either "-la" or "-le". Whereas the "-lü" ending is on 4-way treatment.