Kadabra doesn't actually have a set level at which it evolves. It evolves into Alakazam automatically once it has been traded to another player's "Pokémon" game via link cable or the more recent Player Search System of the Nintendo 3DS.
Kadabra is the second evolution of the Pokémon Abra and can be obtained once Abra reaches level 16. This line of Pokémon is unique not only in how to obtain its final evolution, but also with the fact that the final evolution of the Pokémon can be evolved once more. When using a Mega Stone found in later generation "Pokemon" games, Alakazam can be evolved into Mega Alakazam. However, the Pokémon can only evolve this way when inside a battle, and the evolution fades once the battle is over.