Very cute, and an original take on the theme (using the cube aspect of dice)! I haven't attempted a Rubik's cube in a long time, but I was able to figure it out anyways (with some difficulty). The music is good but it gets a bit repetitive after awhile (although I understand making it longer might have taken more time than you had). Also the dragging to rotate the cube felt a bit off, and pressing space scrolls down the itch.io page on my browser (if you're using plain JavaScript, I think preventDefault is what you'd need to fix this iirc). But overall a good game.
(By the way, if you want to play on Firefox, right click the game, inspect element, find the "body" tag inside the iframe, and uncheck "display: flex")