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This sounds like some anxiety on his part of being left there (it does not necessarily mean he's unhappy) and once you're out of sight, he probably starts crying.
instead of talking to him (at this age is better to use rewards/praise) let him know that when he gets there if he does not cry, he is to earn something (like a favorite treat, small toy, extra play time, stickers etc) but the rewards have to be immediate. Or you could let him know that he could play with something (s special toy etc) while on the way and back from the center if he does not cry.