Securing XBox console from being stolen?

You have the Serial Number from the consoles?

There are custom cases for Xbox with the appropiate holes to let ventilation and disc insertion possible, take a look at this as an example
(not saying it is the right choice for you). With a few of those secured / fixed to a table or something you can prevent that

I have nothing to prevent for console being stolen. Maybe some tracking device in it. If they steal cars, how to prevent somebody from stealing a console? If it is stolen than follow this Link.
It is all we can do for now. Video surveillance? Automatic locking of the doors if the console is moved without knowledge. SF, I know. You, can't put it in some box because it needs air.

I don't remember if the Xbox has a slot for one of these, but you might be able to purchase a Kensington lock for it (I recommend using your favourite search engine to look further into one of these locks). You can purchase Kensington
locks for laptops and many other electronics these days. Basically, it's a metal cable (in many cases, I think) with one end that plugs into the Kensington slot on the Xbox, and you tie the other end to something that would prevent the Xbox from moving too
far.

Regardless of any preventative measures you may put in place, take pictures of the Xbox if it has any markings or features that make it easier to identify. Definitely take a picture of the area where the serial number is located, and also write down that number
and other details in the area of the serial number. If it should be stolen, keep handy your picture and written or other copy of the serial number and other details to show police or other refuge officials to help increase the chances that your Xbox will be
returned.

Acrylic box is a good idea as long as it is drilled for air circulation.

you could bolt a bracket to the shelf to fix the console in place.