My son got this teabag with his motivational pack from Essex University (see earlier tip).
As I'm sure you know, a 'cuppa' is short for 'a cup of tea'.
Why, then, is it pronuounced 'cuppa'?
Because 'of' is a 'function' word - it's not important, so it takes the very weak 'schwa' sound.
You'll hear this in other 'container' words like:
"A bottle of water" (bottluh water).
This Easter weekend, I'm working on my new Pronunciation for Listening Course, which helps you understand what happens in fast, connected speech.
It's still a work in progress, but if you absolutely can't wait, the Workbook is already available in my shop, and the new course will have a video for each lesson.