Filling in holes in a wooden porch frame made by bees
Here are two that come to mind:

Drill the tunnel out to a larger, perfectly round shape. Glue a piece of wood dowel into the hole as a plug. It's not necessary to completely fill the hollowed space -- it would be good enough to make the plug as little as 1/4 inch thick.
Obtain or create some sawdust with a color similar to this wood. Mix it with epoxy, press it into the hole, and place plastic packaging tape over the hole to hold the epoxy (prevent it running out) until the epoxy has set.