This is a Gear Cube twisty puzzle, sometimes branded as a "Perplexing Cube Puzzle"

Mechanism: It features external gears that connect opposite faces, requiring 180-degree turns to rotate. 

Design: The puzzle shown is a black-bodied version with colored stickers (red, green, yellow) on the gear faces. 

Objective: To return the mixed-up puzzle back to its original cubic state.