The answer depends on region and whether you count dual-release Wii/GameCube discs.
The Legend of Zelda: Twilight Princess — November 19, 2006 (same day as Wii launch). This was the final first-party Nintendo GameCube SKU in NA.
Fire Emblem: Path of Radiance — June 20, 2005 (JP) / November 2007 (NA localization). The JP release predates Twilight Princess, but the NA release came after.
Released August 2007 (NA) on a single Wii/GameCube hybrid disc (Wii disc structure but readable by GameCube via backwards compatibility mode). Often excluded from "last GameCube game" lists because it was marketed as a Wii title.