White-backed Woodpecker, (Dendrocopos leucotos owstoni), オーストンオオアカゲラ, or Amami Woodpecker
The Amami Woodpecker has much less white on its back than the Eurasian White-backed Woodpecker. It has less white everywhere else too. It is fairly common here in the forests. The male above has a red cap.
The female Amami Woodpecker has a black cap and less red on the front than the male.