Find all the studs in the outside wall using an electronic stud finder. Mark halfway between each pair of studs using a pencil. Make the marks six inches down from the ceiling.
Cut out circles at each mark using your drill and hole saw bit. Save the cut-out circles.
Set up your insulation blower with cellulose insulation. Thread the blower hose into one of the holes, pushing it in all the way to the bottom of the cavity in the wall.
Start the blower. Gradually fill the cavity with insulation, pulling the hose out as it fills the inside, until you've withdrawn the hose completely. Repeat for each hole, filling the cavities between each pair of studs.
Put a cut-out circle (saved earlier) into on of the holes, setting it so it covers the hole and is flat with the surrounding wall. Put self-adhesive drywall tape over it to help hold it in place. Spread joint compound over the tape using a drywall knife. Get the compound flat and smooth.
Repeat for each hole.
Let the compound dry for six hours. Spread on a second layer of compound over it. Let it dry six hours. Spread on a third coat. Let it dry 12 hours.
Sand the compound smooth using sandpaper, by hand. Repaint the wall.