Sort of: it depends on whether you take the possibility of black holes seriously.
The energy of "some object", i.e. any particular, bounded system, is always bounded (otherwise you have a perpetual motion machine); the energy a given region can contain is not: you can in principle pack as much energy as you want to in to some fixed volume if you're clever enough.
This is within the limits of reason and non-general-relativistic dynamics, of course. If you pack energy so closely that the associated mass, through $E=mc^2$, exceeds the Scharzschild limit, then whatever it is you've got in there will collapse into a black hole and you will lose that energy behind the event horizon.
I should also mention that while black holes look like they have a lot of energy, in fact they do not, in the following sense: the collapse of a star into a black hole is a spontaneous process (i.e. it does not require any action from outside the system) and as such it has to be exothermic, so it will give out some energy as heat, and the total energy inside any box you place around it will at most remain constant. The energy given off comes from the gravitational potential energy associated with stuff being further apart, which you might not have counted in the first place.