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The Rubik's Cube is the most popular puzzle in the world. Two of its studiedaspects are God's Number, the minimum number of turns necessary to solve anystate, and the first law of cubology, a solvability criterion. We modifyprevious statements of the first law of cubology for $n \times n \times n$Rubik's Cubes, and prove necessary and sufficient solvability conditions. Wecompute the order of the Rubik's Cube group and the number of distinctconfigurations of the $n \times n \times n$ Rubik's Cube. Finally, we derive alower bound for God's Number using the group theoretical results and a countingargument.

$n \times n \times n$ Rubik's Cubes and God's Number