I had this happen to my PRe LCI E90. If its under motorplan, take it to BMW, let them fix it.
If it isnt, its quite simple. The dash trim (black) that sourrounds both cupholders is very easy to remove. If I am not mistaken it has 6 clips, use a plastic knife with some light leverage and it should just pop off.
The flaw is in the design actually. Because its collapsible, there is that little piece at the bottom that often clips back when you push it in, in a way that it shouldnt. This is how it gets stuck.
Removing the trim around it, is the only way to access the thing, and see whats causing the jam.
Let me know how it goes.