is there a way to set a boxes texture mode to projected kind of like Sphere.
There is no built in way to do it.
You should do this in a modeling software like blender then import the box in JME.
You have a sphere texture and want to project that onto a cube?
Image transformation to a cube texture might work (precomputed).
A custom shader that maps it at runtime might work (realtime (re)mapping). :chimpanzee_nogood:
Blender - but you will need many and smart subdivisions (many triangles via Blender). :chimpanzee_sad:
A custom mesh with many subdivisions if you like coding it (many triangles via jME/Java). :chimpanzee_sad:
P.S. via baking in Blender you could remap the texture like in precomputed (first idea).
And then … I might miss something, maybe there are other and better ideas…