Just replace the drain plug.

Replace it. Cracked plastic plugs rarely seal right again, and you’ll chase leaks all summer.

You could try epoxy or silicone, but those are temporary fixes. The plug flexes when you open/close the drain, so the repair will crack again. Replacement plugs are a few bucks at any hardware store or Amazon. Measure the hole diameter first — most coolers use a standard size like ½" or ¾". If you can’t find the exact part, a rubber stopper from the plumbing aisle works as a permanent backup.

Future you deserves a cooler that doesn’t leak.