From the Google:

"An error code reading "E81" might indicate a failed update. Turn off your XBox 360 console and turn it back on while holding down the sync button on the console. This should fix all failed update errors."

I have no idea if it will work but it's worth a shot. Another site said you can download any updates and put them on a USB stick and install them that way. That doesn't seem like an Xbox thing, but again, you might try it.