I have a hp 7570i and have just updated the firmware to hp 8100 using the file off this site 8100_10n.bin and can confirm that it works perfectly.
Just incase you are not sure how to do it, this is what I did.
1. download the files from here http://www.cdrinfo.com/tips/hp_oc.shtml
the link is somewhere near the bottom of the page. Then copy the files to a disk
2. print out the readme file
3. make a windows startup disk
4 boot up using the startup disk and then put in the other disk with the firmware on it
5. coose 1 of the 4 combinations from the readme file depending on your setup, but replace the line "100e_10n.bin" with "8100_10n.bin" without the quotes.
For example my cdrw is on 2nd IDE Master, so instead of "updcrx21 100e_10n.bin /at /2 /m" you would put this "updcrx21 8100_10n.bin /at /2 /m" without the quotes ;)