Superglue on its own is not strong enough for this job. The tricks is to sprinkle some baking soda to form an instant cement.
Superglue (Cyanoacrylates, CA) + Baking Soda (Accelerators) = Super-hard instant cement (Exothermic reaction)
Step 1: Baking Soda + Superglue
When baking soda(accelerator) is added, superglue will set almost instantly (5 seconds).
Step 2: Add Few Layers for Stronger Bond
Add superglue to the surface and sprinkle with some baking soda. It will set almost instantly, about 5 seconds. Repeat the steps few more time for stronger bond. Do it on all sides of the broken area.
Step 3: Fixed
The broken part is as strong as original. The surface doesn't shrink, can be sand and paint.