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Material wise you would still have 4 sides of wood (4 pieces), and to make structurally sound, the fit to the center should be OTM to minimize stress to the mitered corners.You could do it, but the glue-up still wouldn't be 4 x 4 due to the size of the basic material.
I've seen columns made by mitering edges thus making a 4 sided mitered column, and you could even build this with a secondary wood as the center.
Bill