6 – Adafruit NeoMatrix boards
https://www.adafruit.com/products/1487

  1 – Female/Female jumper wires – 40 x 6”
https://www.adafruit.com/products/266

1 – Male/Male jumper wires – 40 x 6”
https://www.adafruit.com/products/758

  1 – Arduino UNO
https://www.adafruit.com/product/50

1 – Adafruit Pro Trinket (Optional)
https://www.adafruit.com/products/2000

12 – 1 ½” x 2” pieces of stiff/thin cardboard. The cardboard should be like what you would find on the back of a pad of drawing paper.

Some wire for connecting the sides together.

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Step 1: From the two sets of jumper wires, separate out the red, black, and blue jumper wires. You will have two wires of each color, one female, and one male, for a total of six wires.
Step 2: Cut each jumper wire in half, yielding 12 wires.
Step 3: Solder the jumper wires to the LED boards.
Red to 5V, Black to GND, and Blue to DIN/DOUT..
Female jumper wire for input side, Male jumper wire for output side.

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Step 4: Configure the test software for one board, ie. 64 LEDs.
Load test software into Arduino UNO.
Step 5: Separate out three male/male jumper wires.
Step 6: Plug the three male/male jumpers into the Arduino UNO.
One into 5V, one into GND, and the remaining one into Digital pin 6.
Step 7: Plug the male/male jumpers from the Arduino into the female connectors on one of the LED boards.
Step 8: Power on Arduino, verify LED is displaying correctly.
Step 9: Reconfigure/reload software with another boards worth of LEDs.
2 boards = 128, 3 boards = 192, 4 boards = 256, 5 boards = 320, 6 boards = 384
Step 10: Connect next board
Step 11: Goto step 8, and repeat, until all 6 boards .

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Step 12: Load/run alignment software into Arduino.
Step 13: Pick two sides to connect, and align corners with matching colors.
Step 14: Prepare cardboard connector by folding it longways.
Hold one side of the cardboard under the holes in one of the LED boards and mark the cardboard with pen.
Poke holes through the cardboard, large enough to put the wire through.
Cut wire long enough to go through both holes, with an inch or so through each hole.
Bend wire to slide through the two holes.
Line the cardboard up with the LED board holes again.
Insert/bend the wire though LED board and cardboard.
Repeat this until cube is assembled.

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Step 15: Configure/run animation software and enjoy.Exercise for the reader: Mount Arduino inside of cube, optionally with a battery pack. If you choose to go this route, and you ordered the optional Pro Trinket, you can solder jumper wires on to the trinket, connect it to the cube, load the software on it, etc.