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All you need to do here is shoot the blocks until the sides facing you are blank.
Remove the fog and mist by playing through the Particular Author Quest and solving the puzzles in Shirikoro Peak! This begins a simple floor tile puzzle where you just need to walk around the perimeter first to activate the tiles without jumping or touching the same tile twice.
Turn it on and jump down on your left to find the corridor you were in before.
Stepping on a tile near the cube will activate a puzzle solved by stepping on all the tiles, turning them blue.
You will also be rewarded with three treasure chests.