Why doesn't my sketch start when I'm powering the board with an external power supply?Because the RX pin is unconnected, the bootloader on the board may be seeing garbage data coming in, meaning that it never times out and starts your sketch. Try tying the RX pin to ground with a 10K resistor (or connecting it to the TX pin).
First and foremost, what part of "not for problems with your project" at the top of this forum section was unclear? This is a problem with your project, not the Arduino itself.
If you press the reset button on the Arduino after powering it on, does that fix the problem? If so, try putting a delay at the start of the sketch before initializing the LED controller.
Do the driver chips for the LED cube have a reset pin?
Can you confirm that the sketch is actually running? You should see the pin flicker when sending SPI data, as that's the SCK pin..
Do you have an external pullup on the CS pin? If not, install one - 10k is sufficient.
It is... choose one, and click report to mod in the other one as ask for its removal.
This is indeed a violation of the rules as not every person that answers your questions reads both forums so if two different people answer your different version of the same query with what will most likely be the same information, you have received more than your fair share of attention and wasted the time of one or the other (or both?).
Further, you are even cross posting on this form as you have made a new post about the same project and problem, requiring people to go and find the other (previous) topic if they wish to know adequate details regarding what on earth it is you are doing as a prerequisite for a sensible answer!
Have you tried reducing the SPI speed? I seem to remember from your previous topic that was set to 8MHz,.....