Remove as much of the damaged wood as you can from the base of the pillar with a chisel and hammer. Cut any deeper rotted material from the pillar with a circular saw. Allow any wet wood to dry overnight.
Measure the sides of the pillar with a tape measure. Cut four pieces of 3/4-inch thick molding, tall enough to cover the damaged area at the base of the pillar 1.5 inches longer than the width of the pillar.
Stand the molding on the miter saw with the bottom on the table and the back against the fence. Cut 45 degree miters at each end of each piece of molding, one right and one left, angled out, so that the long points of the miters are on the face of the molding.
Apply glue to the back face of the molding. Align the molding with the faces of the pillar, with the inside corners of the miters on the corners of the pillar. Nail the molding in place with 1 1/2 inch pin nails, one every 4 inches.
Open a large syringe and fill it with industrial strength exterior wood glue. Inject glue into every crack to fill it until the glue seeps out slightly.
Fit one strap style clamp just above the damaged area. Thread the strap through the buckle of the clamp and ratchet the clamp snug. Fit a second strap clamp around the pillar just below the damaged area and snug it up. Alternate tightening the top and bottom clamps, one ratchet at a time until the cracks close.
Use a wet rag to wipe excess glue from the surface of the pillar. Allow the glue to harden for 24 hours. Sand the face of the pillar with a power sander with 150-grit sandpaper to smooth the repair.