Can't connect to Xbox live after update on 360

8007-2746 means you're having a connectivity issue.

Its a "lovely" cycle - can't update cause it needs to connect to live, can't connect because it needs an update but can't update until it connects to live.

You can try manually installing by going to support.xbox.com and searching for console update - "Update your xbox 360 console" will have the information you need.

Hi there,

please try the steps on the following link to try and solve the connection issue on the 360, this link will have several things to try and get the console connected again.

Link:
connection-solution

Let us know the results

I was able to finally update my XBOX 360 but I still can't connect to XBOX Live.

same here, my lounge xbox can't download the update because it can't connect to live. my bedroom xbox downloaded the update after trying to connect to live a few times. my bedroom xbox, though, can't connect to live now either and it's been updated, whats
with that? we've been tryna clock gears3 on insane over live, but now we're just gonna watch movies from the rental shop. stink.

Hello

Try the solutions below if the Xbox 360 console software doesn’t update successfully, and you get one of the following error messages:

• Can't download the update. To test your connection, open System Settings and select Network Settings, Test Xbox LIVE Connection.
  
• Can't install the update. The disc is unreadable.
• Can't read the update from the disc. Please reinsert the disc to continue the update.
  

If you get an error code such as xxxx-xxxx-xxxx-xxxx-C000-0001 (six groups of four-digits), please see Error code after Xbox 360 update.

http://support.xbox.com/en-US/xbox-360/system-updates/system-update-help