Hi Violet,
I am by no means an expert on consoles, but this might be a starting point in your struggle.
XBox (I have one and had a similar problem with updating), will periodically check if it needs updates. The new game may have triggered this.
It gets its updates via the internet, from the microsoft site.
To do this, it needs to be connected to the internet via a router, either via wifi or cable. I am assuming you have a router for internet/broadband at home.
Some (possibly all) routers block certain types of traffic and/or on-line games. Minecraft may be one of them.
So you/or your son need to do a bit of digging/searching in google for the correct sequence to open (if only temporarily) the router to allow the update to download.
You need the following
1. A broadband/internet router (I assume you have one.)
2. The ability/knowledge via your PC to get to the router configuration page to open the required traffic to allow the Xbox to update (this is where Google will give you the step by step guide to do so).
If you/your son don't feel comfortable doing this you have a couple of options.
1. Bring his xbox to a friends house who already has the ability to download the updates.
2. Bring the xbox to somewhere like PCworld or Currys that may be able to download the update.
3. Get one of his friends around that knows about the router/configuration settings and get him to do the necessary. (He's bound to have one computer savvy friend).
When I had to do it it took a while to get it right, but it will only have to be done once, and the google search gave up pretty straightforwards step by step instructions.
Hope this helps.
Corkboy