no, that's not my case.
This treatment is almost equal to my reference book: http://qfizik.upm.edu.my/phy3601/lecture05.pdf page 5.
You see that the condition is not ψ(x, y, z)=ψ(x+L, y, z)=ψ(x, y+L, z)=ψ(x, y, z+L)=0, but the value at the boundary can be non-zero. So there can't be an analogy...