As you don't show a picture then I will be making some assumptions.

I would be doing one of the following:

1. make the hole circular and glue in a dowel then surface to suit.

2. screw in some screws such that they are below the surface and protrude into the hole to be filled. Use a "stiff" mix ie one that won't sag and fill then treat as needed to match the surface.

As you don't show a picture then I will be making some assumptions.

I would be doing one of the following:

1. make the hole circular and glue in a dowel then surface to suit.

2. screw in some screws such that they are below the surface and protrude into the hole to be filled. Use a "stiff" mix ie one that won't sag and fill then treat as needed to match the surface.

Edit, based on the picture now posted: I have repaired damage like that by drilling a hole for a dowel and once fitted then drilling the next dowel so it overlaps the first. Continue so you have a set of overlapping dowels that "lock" in to each other. Surface to suit. Once completed and painted it was indistinguishable.