Translation:Would you like to go get a cup of coffee?
Are you sure this is true for the AmE and BrE? (I'm not that native, but i think i heard it quite often...)
As a speaker of AmE, I've never heard anyone say "Would you like to take a coffee?"
We do say: "How do you take your coffee?" => "What do you take in your coffee...milk or sugar, or do you take it black?"
I have coffee in the morning and take my coffee black with a lot of sugar.
British English you can say: Would you take a coffee? But with the 'like' it would more commonly be: Would you like to have a coffee? Would you like to take a coffee? seems ok too, to me, but less common.
In the states I would more often hear, " Would you like to go for coffee,", rather than "to go get".
If i put " would you like to drink a Cup of coffee " also is correct ?
We use "drink coffee" for general statements.
• How many cups of coffee do you drink a day?
• Do you drink coffee after dinner?
To invite someone for coffee:
• Let's get/have some coffee. (informal)
• Shall we get/go get some coffee?
This is very poor and unused english if you are not american. it is purely an american idiom "go get" the rest of the english speaking world would not say that.
"Would you like drinking" should also be accepted. It has no difference and means the same thing as "would you like to drink." But "would you like to go get a cup of coffee" makes no sense and does not correspond to this sentence. In that case it would be "Você gostaria pegar uma xícara de café?"
"Would you like" requires the infinitive form, not a gerund. I think that you are confusing "do you like" with "would you like."