New Berlin Colony was a Federation colony. It was in the same sector as the Ohniaka system and the MS system.
In 2369, there were heightened tensions due to Borg activity. When a Ferengi trading ship entered New Berlin's star system, the colony panicked and sent a distress call. The USS Enterprise-D received the call, but it was quickly cancelled when the ship was identified. The Enterprise acknowledged the colony's signal and transmitted them a copy of the Starfleet ship-recognition protocols, with a suggestion that the colonists read it. (TNG: "Descent")
This colony was only mentioned in dialogue.
According to StarTrek.com, this colony was named after Berlin.[1](X) The Mazurka Festival, attended by Calvin Hudson, Benjamin Sisko, and their wives, was said by this website to have occurred here, not at the settlement of New Berlin on Luna.