A simpler way to create a cube with tubed edges:
Graphics3D[Tube[#,.05]&@@@PolyhedronData["Cube","Lines"],Boxed->False]
Perhaps then if Texture is a simple small square shape and VertexTextureCoordinates is used to repeat it different number of times in different directions, then separation of the Texture for vertical and horizontal would not be needed. But this needs testing.
