Can I bake a christmas cake in a cardboard box?
While there is some possibility it could work, I wouldn't even try it. There are things that can go wrong, and many proven solutions to the problem. Replacing a bad hack (newspaper) with a worse hack (cardboard box) is not something I would be keen to try.
A list of preferred solution includes:

use cake strips
bake the cake in a different pan (bundt or thick-walled ceramic pan)
go for a flatter and wider cake (bake it in a quiche pan or a large tawa)
make it a layered cake and bake the layers separately
reduce the temperature and bake for longer
partially bake in a waterbath, then continue without it

If you are absolutely sure that your cake needs a full enclosure (which is quite strange for me - it is actually one of the reasons why I would avoid the cardboard box) I would prefer putting the cake in a roasting dish (earthenware/ceramic or metal) rather than in a cardboard box.