cubemania.org
It's very nice and keeps graphs of your averages. You also have an account so it can save all your times and they are accessible from any computer. Only downside is that it only keeps averages of 5.
I had the same problem you're having but it was with youtube. I asked about it on yahoo answers. This is what I got:
If "your browser sent a request that this server could not understand"
plus "Size of request header field exceeds server limit", that request
is a bad or oversized cookie. (The same thing is true for "Error 400").
For some very strange reason, it seems that
most Bad Request messages involve Firefox.
Simply delete your "Cookies" and everything
will be okay. Don't worry about erasing them;
nothing bad will happen. You won't lose your
internet browser's "Bookmarks" or "Favorites".
The worst thing that could happen is you will
be asked to retype your username/password
when you return to YouTube and some other
websites -- that's all.
Just as important, you should also delete all
your "Temporary Internet Files" and "History".
Those steps will make your computer totally
"fresh" in YouTube's eyes and make loading
and buffering faster. It would also be better if
you shutdown/reboot after doing this:
Mozilla Firefox 3:
→ Tools → Clear Private Data
[x] Browsing History
[x] Download History
[x] Saved Form and Search History
[x] Cache
[x] Cookies
→ Clear Private Data Now
It worked for me. Though I would still recommend using cubemania over cubetimer, it is much more organized.