Usually, dense foam wrapped in poly fiber is used for the core of box shaped cushions. You an buy pre-cut pieces or sheets of 3 to 4 inch foam for the cushions and poly fiber (sold by the yard) at Joann's or from an upholsterer's supply shop.
If you want thinner cushions, you can use thinner foam wrapped in poly fiber.
If you want to make cushions that will be out in the rain, there is some foam that has holes through it for drainage. Supposedly it doesnt mildew, but I havent tried it.
The best fabric to use for any cushions that will be exposed to weather is Sunbrella or a similar fabric. Also available at Joann's or similar fabric stores.
Hint: Stuffing the fiber wrapped foam into the covers is easier if you first wrap a plastic garbage bag around the cushion. The garbage bag is then pulled out before the cover is zipped or sewn closed.