Yes Superman can break adamantium. Adamantium is not unbreakable, it's "virtually" indestructable.
http://marvel.com/universe/Adamantium
Marvel wiki states "Virtually" indestructable. Words have meaning, "virtually" does not mean completely and or totally. It means "nearly" or "almost entirely."
Since Superman can shatter the boundries of space/time with the shockwaves of his punches, (see Superman Infinite Crisis tie in issue)he can break the "virtually" indestructable Adamantium under his normal power levels. If he somehow could not do so under normal power levels, then he most certainly can after a sun bath.
I've noticed many comic book readers make untrue claims of Adamantium being unbreakable or (another example) Hulk having "limitless" strength. When Marvel states Adamantium is "virtually" indestructable and Hulk has the "potential" of limitless strength. "Potential" means basically possible, not actual.