Would you like some coffee?& what about some coffe?
where are the difference
What situation use them

Question

Would you like some coffee?& what about some coffe? 
where are the difference
What situation use them

Answer

"Would you like (to have) some coffee?" is more polite mostly used.

You don't say "What about..." you should say:

"How about some coffee?"

"What about x" actually means 'what is your opinion/remark about x'

Answer

Mostly people use " Would you like to have some coffee?" It is the polite way of asking the guest.
There is no much difference between the first and second.