The direct way to do this is to use Proportional Editing set to Random.
You can activate Proportional Editing, in Edit Mode, by pressing O while your mouse cursor is over the 3d Viewer. Or, you can go to the bottom menu bar and click on the button in the middle, with the little gray circle in it, as shown in the gif movie. You want the Random setting in the pop-up.
Then select any vertex, and press G to move it. When Proportional Editing is active, a circle appears around the cursor showing the range within which it affects the mesh. You can increase and decrease that distance by rolling the mouse wheel up and down. I just made it big enough to surround the whole cube, and shifted a vertex a bit. Then I did that a few times, selecting different vertices and shifting in different directions.