AI would use rice krispies treat, made and crumb coated separately. Then after your gift box cake is done, place it on top supported by a cardboard and dowel or bubble tea straw. You can even add the "fur" by piping brown "fur" after you have placed the bear on the cake so it doesn't get smudged duribg assembly.
I would use an all butter or a meringue base frosting though for crumbcoat to the bear and the fur because when a crusting BC dries/crusts the fur will have a hard time adhering to the bear and will keep falling off when you're trying to pipe it. Especially the fur on the sides and bottom of the paw..HTH! Good luck! Very cute cake :)
If you are really wanting the teddy bear to be cake you can either carve by hand with a really sharp bread knife or use the wilton soccer ball pan for the head and add fondant decorations and buttercream fur as suggested already. The "paper" is probably modeling chocolate as it is firm but moldable.