you are going to have to use poly's mate. When you create a nurbs cube/cylinder/cone all of the different square sides are separate surfaces. So a cube would have 6 detachable surfaces, a cylinder has 3 - the 2 caps and the cylinder tube - and a cone 2.
As you extruded your cube along the path you can also do with a poly.
BUT if you want to stick with nurbs use a nurbs square and extrude it the length of the path. Then you will have a 4 sided wire, no end caps but you can create those with a planar of the square.

Does that help?