The trick is to use a cardboard jig to keep the wooden cube aligned during each of the engraving steps so that the patterns on the edge of the cube match up perfectly.
Step 1: Create the Pattern
This particular file assumes that you've got a 1.25" cube, but you can obviously scale it to fit whatever size block you've got.
In the .CDR file there is a black/white raster image of the companion cube itself, and there is also a hairline thin square that overlays with the cube. That square is what you will use to cut a jig in your sheet of cardboard. (As will be magically revealed in the next step!)
Step 2: Cut a Jig
Make sure that the cardboard is held down and won't move at all during future steps, (I slipped the cardboard under the left/top spring-loaded rulers.)
Load up the .CDR and hit print. In the print settings you'll want to set it to vector cutting (we'll do the raster engraving later) and set the power/speed/dpi appropriately. For my 60W laser cutter I use 100% speed, 80% power, 600DPI for cutting through cardboard sheets.
After the cut is done, carefully remove the square of cardboard but make sure you don't move the cardboard sheet. The whole point here is to have a jig that we know with absolute certainty is aligned with the raster portion of our image.
Once the square has been removed you can insert your wooden cube into the jig. You may have to play around with the scaling of your square to perfectly fit your particular wooden cubes. You want the cube to slide into the jig effortlessly, but to have the smallest possible room to jiggle around. Make sure that you test multiple orientations of the cube to make sure that they all fit.
Step 3: Engrave, Rotate, Repeat
Adjust the focus on your laser cutter to the height of the cube (rather than the height of the cardboard.)
Hit print again, but this time in the settings choose Raster mode and adjust the settings to 100% speed, 40% power, 600 DPI. (Adjust as needed based on your machine.) You can also try 100% speed, 80% power, 300 DPI if you want a slightly lighter cut that finishes faster.
Engrave away and watch the companion cube magically appear!
After it finishes, carefully remove the cube from the jig, rotate it, and reinsert it back into the jig.
Repeat 6 times. Dance with glee.
Step 4: Enjoy
If you want to cut a bunch of cubes at the same time you can cut multiple jigs in your cardboard and load up a bunch of cubes to engrave in parallel. If they're all in a line horizontally then they will engrave much faster then they would individually.
These blocks have recently been tested by both a 2 year old and a 2 week old and they have received favorable reviews from both.
I'm going to be posting a series of different cube instructables and I'd love to hear any ideas you may have for other cubes.