Before we can give you a useful answer, you must tell us what kind of
construction and materials are involved.
You may want to do several things, since wall assemblies are usually
made up of several layers of different materials.
Trying to put some wiring in an outside wall, I drilled down from the
attic and came out the wall to the outside about a foot below the
roof, on the second floor!! I was annoyed at myself, but the house is
dark brown, the same color as one of those caulks, and I put in 20
years ago, and I've never noticed the hole again. That stuff is
match, will take care of the outside hole. Maybe shove a little
fiberglass in with a screwdriver to block the air path, or use
foam-in-a-can, if you have some other projects that need doing. (Once
you start those cans, forget about putting them back on the shelf.)
Inside, a dab of spackle will cover the hole.
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