Remove all modifiers from the cube and start again.
First, add a Bevel modifier. This gives supporting geometry, so when you add a Subdivision Surface modifier, the cube doesn't turn into a sphere (Try for yourself if you don't believe me).
So, add the Subdivision Surface modifier next, (this gives extra geometry to displace - I set number of subdivisions to 3 to start).
Lastly, add the Displace modifier, pick the cloud texture, set the strength to 0.5 and you should get this:
So, the order of modifiers (from top to bottom) is Bevel, Subdivision Surface, and lastly, Displace. You can control the detail of the clouds by increasing the subdivisions of the Subdivision Surface modifier.
If you need to triangulate, you can add a Triangulate modifier afterwards.
EDIT- Is this more to your liking?
If so, all I did was subdivide the cube once, then I placed a Bevel, Displace, and Triangulate modifier in the order shown. You can play with both the Bevel values as well as the Displacement Strength and Midlevel to get different shapes and sizes.
As for the colors - they are in user preferences - Theme is "GreenHorizon"