Why isn't cái used in this sentence? What is the difference between "Một ca cà phê" and "Một cái ca cà phê"?
Same meaning, simply you can skip "cái" when you speak or write in this case. Some time you must to put "cái" in the sentence, example:
Give me a glove: Đưa cho tôi cái găng tay.
But if you say backward in VNese (same that English sentence): Đưa cái găng tay cho tôi = Đưa găng tay cho tôi.
I'm VNese and I find this hard to explane, even my teacher ; _ ; hope this helpful...
Please take a look at the word 'of' in English http://www.ldoceonline.com/dictionary/of. I'll try to answer your question using the link above.
Most of the time, OF means CỦA (belong to someone/something) [Meaning 1, 2, and 3 in the link]
OF means TRONG, TRONG SỐ (among, between) [Meaning 4]
OF means CHỨA (contain) [Meaning 6] -> CHỨA can be left out
the rest are much more complicated so leave them for later exploration ;)
As you can see: 'a mug of coffee' -> Meaning 6 in the link -> OF means CHỨA -> You can translate the sentence as 'một ca CHỨA cà phê', or simply 'một ca cà phê'. CHỨA can be left out. ;)