Pouring concrete

I have an outside grill that is set in blocks. These blocks are the type used to build a seat wall or pillars around a patio. The grill base was built at the time the patio was laid, which is made out of pacers. So the grill is built on top of a sand and gravel base. The grill has stainless steel doors that open for storage and to turn on the gas. I want to pour concrete inside the base and have a level floor for storage. My question is, can I por concrete inside the grill base? Will the concrete expand and push out the block? The block itself is about 10 inches thick, and is solid. So the overall space that would be filled is about 4-5 square feet. Also can I just por the concrete on the sand/ gravel base? Will I need to dig down? I don't think the winter will cause it to heave if it is poured on the sand/ gravel base? Please help if you can