You are only allowed into the Embassy through the front door during the Diplomatic Immunity quest because you have an invitation.
Without console commands (if you are on a PC) you can't enter the main building(s) again through any door once you have left it at the end of that quest.
I did read something about being able to get back in through Reeking Cave (this is the way you got out if you left through the trap door in the torture dungeon). You have to jump down from a ledge to get out of there, but supposedly if you positioned yourself properly you could Whirlwind Sprint yourself back up onto the ledge and retrace your steps to the trap door, if you have the key to that you can go back into the Solar/dungeon that way.
But finding Reeking Cave again can be difficult as it doesn't appear to be marked on the map at all, I had to memorize its location the last time around so I could get back there. And when I did, no matter what I tried I could NOT shout myself back up onto the ledge. So that may have been changed in a patch, which is not unlikely since the biggest complaint seemed to be that people needed to get the Stone of Barenziah that they missed when they were in there on the MQ. One of the patches moved the Stone to the lower part of Reeking Cave so there is no quest-related reason to get back into the Embassy, maybe they redesigned the cave to make it completely impossible, I don't know.
If you are on PC you can just use the console to unlock the front door or turn off collision and walk through the wall, if not, I don't think you can get back in unless you can find Reeking Cave and have better luck backtracking through there than I did.