Have you seen a vet to rule out health issues? That's a first because cats can have serious health issues that are often mistaken for behavior issues. If your cat is urinating outside of the box and is a male in particular he may be suffering from a urinary tract infection or UTI. You have to catch those quickly and go to a vet early. If not there's a risk that your cat will die from blockage in his system. They're common and deadly but easily remedied by a vet so better to err on the side of caution with those things.
After that it could a number of things. Have you just tried putting the box in your cat's new favorite spot? Maybe it's the scenery there!
Part of the trouble with animals pottying in inappropriate places is that even though we clean up the spots and think we've got it all, there's still some residue left that their superior noses can detect. Grab a black light and shine it in your basement. That will show any spots you may have missed because urine will glow under a black light. Cool huh? Then you need to use an enzymatic cleaner to hit those spots. You can buy those at a pet store or just surf this forum for people's inexpensive recipes.