I had a friend who did rubix cubes (fast, but not blind. also digital ones with extra dimensions). I think they memorize the sequence to do, not the actual colours on each cube. so it's like when people memorize a really long series of cards, except they need to work out what the cards are, but they have fewer cards and some sequences are impossible.
according to wikipedia, the longest optimal solution for a rubix cube is 20 moves. since some are shorter, but they probably don't usually get the best solution, for 50 cubes it's kinda like they're memorizing 1000 cards in sets of 20ish. 1924 cards (divided into decks) is the record for cards memorized in an hour at the world memory championships. so they're not actually memorizing that much and have lower penalties for messing up. I wonder if they are allowed to use notes to aid their memorization. if they are, it's actually way less impressive than the cards: go cube by cube and make notes, then memorize notes, then solve the cubes. if they aren't, it's amazing that they can work out the cubes without forgetting the previous ones.