What Are the Energy Levels and Degeneracies for a 3D Cubical Box?

[cytochrome]

Homework Statement

Find the energies of the second, third, fourth, and fifth levels for the three-dimensional cubical box. Which are degenerate?

Homework Equations

E = h^2/8mL^2 (n^2 sub x + n^2 sub y + n^2 sub z)

The Attempt at a Solution

The levels would be degenerate if one of them occupied two or more different states, or if two occupied the same state, correct?

I'm lost on what to use for n_subx, n_suby, and n_subz in the problem. I'm pretty sure it's not Pythagorean

 

[cytochrome]

I've found that (1,1,1) = 3, (1,1,2) = 6

and 6 is degenerate since it could be (1,2,1) or (2,1,1).

But do these correspond to n = 3 and n = 6?

 

[clamtrox]

n_x, n_y and n_z are positive integers, so 1, 2, 3,...

Clearly (1,1,1) is the ground state, and (1,1,2) is the first excited state. What's the second one? Is it (1,2,2) or (1,1,3)?