I long for drinking a cup of coffee.
&
I would like to drink a cup of coffee.

What is the difference?

Question

I long for drinking a cup of coffee.
&
I would like to drink a cup of coffee.

What is the difference?

Answer

A "longing" is a STRONG desire.

Answer

You can think of long as a version of want/desire. I don't think you've used it grammatically correctly, it should either be:

I long to drink a cup of coffee
or
I long for a cup of coffee

It's a more forceful desire than is conveyed by like (as in your second sentence) or want.