We have our first European (or Arabic, depending on how you see it) loanword in Duolingo Vietnamese! Cà phê comes from the French café, also meaning coffee. The English word coffee comes from the Dutch word koffie, and both koffie and café come from the Italian caffè, which comes from the Turkish kahve, which ultimately comes from the Arabic قَهْوَة (qahwa).
"In turn, the Arabic qahwah may be an origin, traditionally held to refer to a type of wine whose etymology is given by Arab lexicographers as deriving from the verb qahā, "to lack hunger", in reference to the drink's reputation as an appetite suppressant." (https://en.wikipedia.org/wiki/Coffee#Etymology)
"The Arabic word has been said to originally have referred to wine, although some sources instead claim it traces back to the name of the Kaffa region of Ethiopia, which is an Omotic word." (https://en.wiktionary.org/wiki/coffee#Etymology)
Both sources seem pretty sure about the Turkish origin though.
It is very interesting!
Now I am guessing about the pronunciation of cà phê. And it is similar to the form that people offer coffee to the public in Buenos Aires, Argentina. "¡Café! ¡Café! (pause)... ¡Café! ¡Café!", say vendors. =)
I see also that cà phê is very similar to the Thai คาเฟ่ [Khāfè], that means cafe (in Vietnamese quán cà phê), and a bit different to กาแฟ [Kāfæ], that means coffee.
It's a loanword in a few East Asian languages as well. These are the ones I know about:
In Mandarin and Cantonese - http://forvo.com/word/%E5%92%96%E5%95%A1/#zh - it's "kāfēi" and "ga-fē" respectively.
In Korean, they don't have an "f" sound, so they use an aspirated "p" (커피) - http://forvo.com/word/%EC%BB%A4%ED%94%BC/#ko
I haven't studied much Japanese so far, but again "coffee" is a loanword (コーヒー) - http://forvo.com/word/%E3%82%B3%E3%83%BC%E3%83%92%E3%83%BC/#ja
As far as I'm concerned, "cái ca cà phê" is often implied as the mug which filled with coffee, because you cannot really know which mug is specified for which purpose. It is possible to translate this phrase as both, but it is more often intepreted as the mug filled with coffee.
No one should ever drink that much coffee in one day! Not recommended, Lol! BTW, how would people say "a jug/pitcher of water" in the North? I live in the South but my dad is from the North. He would use "ca" for a jug/pitcher just as my mom does. She was born and raised in the South. Vậy người Bắc thường dùng từ gì để mô tả cái ca đựng nước? Mình cũng thắc mắc lắm đây!
I always use (and hear people use) in the North the word: "cốc nước" for mugs/big cups of water. And for a small cup, we use "chén nước". For pitchers, it should be something like "bình nước". Từ "ca" làm mình nghĩ đến cái ca nhôm/sắt mà ngày xưa ở miền Bắc người ta thường dùng trong thời kì bao cấp :-)
The preposition "of" can have various meanings in Vietnamese such as: của, thuộc về, thuộc loại, chứa, đựng, dùng để uống etc. In this sentence, you can translated "of" as "chứa/đựng/dùng để uống" -> "a mug OF coffee" = "một cái ca CHỨA/ĐỰNG/DÙNG ĐỂ UỐNG cà phê". However, in daily conversations native speakers just omit "of".