“Can you…” conveys somewhat of an intention to order something, in a slightly more polite way than an order itself, like “Can you close the door on your way out, please?”, meaning “Close the door on your way out, or I’ll be disappointed by your failure to comply with this”.
“Could you…” allows for a more compassionate tone: “Could you close the door on your way out, please?”, meaning “I would really appreciate it if you would close the door on your way out/it would make things easier for me if you did that”, it’s like posing the question in a more positive way.
But you may also use “may” or “might”, even better for polite requests: “May you close the door on your way out, please?” is even more delicate and certainly polite. If you want to have a chat to improve your English, send me a message!