My xbox 360 showed error code 3080-3151-b200-0700-c000-0059 and system update stopped

According to the link below, if you scroll all the way down, the last entry in the table shows for your error, that you need to contact the Xbox Support.

Just visit the link below:

Xbox 360 system update error codes

This is very simple: you seem to not have enough hard drive space for a system update that your console is trying to install.

Error 8007 0070 occurs when you install an update or buy content on...

(I've pasted some bullet points for you)

" Error 8007-0070 occurs when you install an update or buy content on Xbox 360
Problem
You may see the following error code and message when you try to update your Xbox 360 console or purchase content:
xxxx-xxxx-xxxx-xxxx-8007-0070

Note The "x" characters in the error code vary.
This may mean that there's not enough space on your storage device (mostly likely the Xbox 360 hard disk) to install the update or the content.

Solution
A console update or content download may require significant hard disk space. If you don't have enough free space, you need to move or delete some items."


You can probably get around this by using a 32gb USB thumb drive and moving some of your content that's hogging up your console's space onto that thumb drive temporarily.

Heres the Xbox.com info to get you started about moving and deleting hdd space--which also has info about using a USB thumb drive, too. Copy move or delete Xbox saved games profiles and avatar items

Xbox.com has a handy search page to lookup error codes:
http://support.xbox.com/en-US/error-code-lookup

From that page, those is the answer and resolution they give, good luck:
" Error C000-000E occurs when you try to download an update to your Xbox 360 console
Problem
You see the following error when you try to download an update to your Xbox 360 console:
error code xxxx-xxxx-xxxx-xxxx-C000-000E
Update failed.
Note In this error code, the "x" digits vary.
This error message means your console could not download a software update from Xbox Live.
Solutions
To resolve this problem, try the following solutions:
Solution 1: Try installing the update again.
Solution 2: If you're having problems connecting or staying connected to Xbox Live, see Troubleshoot your Xbox Live connection.
Note You can also update your console software by copying the update to a USB flash drive or a disc and then applying it to the console. "

Does the Xbox power on with no disc inserted? If so, connect it to your network and run a system update over the internet. The version on disc is probably out of date and might not be compatible with the version currently on your Xbox.

I got this from the Xbox support site for your error code.

Error Code xxxx-xxxx-xxxx-xxxx-8007-045D
A storage device (such as a memory unit or hard drive) was not found during the software update. Follow these steps:

1. Turn off your console.
2. Remove all console storage devices, including any USB flash drives, external hard drives or the internal hard drive on the Xbox 360 E console or Xbox 360 S console. Learn how to remove the hard drive.
3. Add your primary storage device, for example, the hard drive.
4. Turn on the console
5. Try updating the console again.

Here's the website if you wish to peruse it further.
http://support.xbox.com/en-US/xbox-360/system/software-update-errors

Post back how it works out!
http://support.xbox.com/en-US/xbox-360/system/software-update-errors

You need to contact Xbox Phone Support team... You can reach them here: support.xbox.com/contact-us

Probably because its a pirated game, and you are trying to run it off of a modded xbox. Try disabling the mod updating your mod, and 360. Then try playing the game.

If this is an error while trying to update your system, follow the link below and attempt to update your system using the USB method

http://support.xbox.com/en-us/pages/xbox-360/how-to/update-xbox-360/system-updates.aspx