How to repair a damaged seam on leather sofa

You cannot "fix" it without replacing the floorboard, but you can patch it to look close.

That looks like IKEA's pressboard laminate - that's not wood you're seeing, that's paper. You can check their stock for some extra boards if there's one near by - sometimes they might have some extras in returns.

So - get yourself some dark stained wood filler and a 2" putty knife, and a small "wood stain marker" that matches the color more exactly. You can find all of these in among the paint aisles in any big box hardware store. You'll also want some 100 grit and 220 grit sandpaper.

Fill the hole with filler and smooth with the knife. Let it dry and sand smooth first with the 100 grit then the 220 grit.

Finally, stain the filler to match, and let dry.

Replacing is probably most practical.

But if you really want to fix it, you need something to support the weight. Tape and glue aren't going to do it. I would find a length of strong pipe (check the plumbing section at a home improvement store) that will fit nicely either inside the leg (if it is hollow) or over top of it. Make the pipe fill/cover as much of the leg as possible. Then attach with tape, glue, bolts, whatever - just to stop it from sliding out.

If the pipe fits snugly it should hold up fairly well.