I agree with Cyn, cardboard gets wet and stays wet, and if you've got a block building and weather cold enough to want to insulate, chances are real high it will get damp from condensation where it contacts the block wall (it isn't really that good an insulator).
Better would be to put plywood over the cinderblock (preferably flush against it, rather than on studs, unless you want a mouse farm -- although on studs, if you put fiberglass batts or foamboard behind it, will certainly give you much better insulation, tho at greater expense as well).
That will also help keep the coop air MUCH MUCH drier. The difficulty with cinderblock walls in any but a very dry-air climate is that they have lots of thermal inertia and every time you have a bit of warm air coming in, from mid-winter to mid-spring, it condenses out and makes the air indoors really unhealthily humid.
I suppose you could even use OSB (chipboard), being cheaper -- although it will not hold up over time as well as plywood.
Good luck,
Pat