In my backyard, Red-bellied Woodpeckers go nuts for peanut halves that I provide in a hanging feeder and on a platform. They usually drop in for one peanut at a time and then they fly away to eat it or cache it.
Their second favorite food at my feeding stations is suet. I use one of those hanging suet feeders with the little wooden paddle on the bottom. Woodpeckers can brace their tail against it which makes it more comfortable for them to eat (like they are braced on a tree trunk).
Red-bellied Woodpeckers will also eat black oil and hulled sunflower seeds, safflower and cracked corn. When I have dried fruit that’s getting a little tough, I put that on the feeders and these birds will gobble it all up.
In the spring I’ve also seen them nibble the orange halves and eat the grape jelly I put out for the Baltimore Orioles.
We never saw Red-bellied Woodpeckers when I was growing up in southern Wisconsin, but over the last several decades their range has expanded much further north.