How to add a lattice on cube's surface? I made a single lattice around a cube in the following way: 


Added a cube on scene.
In Edit mode I added loopcut with Ctrl+R.
Removed corner vertices.
Converted the cube to curve.
In Object Data tab I changed geometry properties and received next object: 




Now I need to make double lattice like this(left side):



But when I made double lattice by previous way I have got object shown in the right side of previous picture.
How can I get a required object?
May be exists better way to make this objects?
You can either use the wireframe modifier or the skin modifier:

For Wireframe modifier:


Add Cube
Subdivide with 2 divisions
delete edge vertices
add wireframe modifier


For skin modifier:


Add Cube
Subdivide with 2 divisions
delete edge vertices
delete all faces (faces only!)
apply skin modifier
Scale with ctrla