The cupholder in the E38s are a weak spot and are one of the most common failure points in these cars. In fact, when speaking to owners, many have given up on these because they are not easy or cheap to replace with the OE parts, and they usually fail a second time.
Several people have installed the aftermarket unit from places like
www.cupholders.com.
If you wish to replace the unit with one from BMW it requires that the center console units all be removed starting fromt he radio on top and working down to the switch panel. The cupholder is mounted ot the plastic frame that is called the "console carrier" from the bottom, so once the units are all out of the carrier frame, then the frame itself is removed and the cupholder unit is removed and reinstalled to the frame.
The best source for these types of repair instructions is the TIS CD-ROM. They are sold on ebay all the time for a few $$ and there is an image file available for free on the web at:
ftp://ilovemybmw.com
the user name is: bimmer
password is: e38power
Install password is: berlin56
If you don't know how to use the ftp protocals then this the peer to peer service at
www.edonkey2000.com
I know there are several CD images to download for free of the TIS (repair manuals) and ETK(parts catalog) CDs here.