Sigma Palace is the name given to Sigma's base of operations in both Mega Man X1 and 8.
Mega Man X[]
In X1, Sigma was master of a gigantic fortress which floated in the air a short distance above the sea. It was heavily defended by a vast army of Mechaniloids and each section of the base was protected by a mindless replica of one of Sigma's Maverick lieutenants that had been destroyed by Mega Man X. After X defeated Sigma, the fortress self-destructed and sank beneath the waves.
Mega Man X8[]
In MMX8, Sigma's forces built him a castle on the surface of the Moon. From here, Sigma orchestrated the corruption of the Jakob Project and prevented the human race from colonizing the Moon, forcing them to remain on Earth until Sigma devised a method to destroy the whole planet. This palace was not as heavily defended as his first base during his original rebellion and was only protected by a small force of Guardroids. The Guardroids were capable of taking on Sigma's form, however, increasing their combat effectiveness. When Sigma and Lumine were defeated, the palace was left vacant. It is unknown if it was ever demolished but no such destruction was seen in the ending to X8.