AWGs for the following LED setup
As you realized, the maximum current would be 10 A at 12 V.
According to the engineering toolbox website this would require a 16 AWG copper cable (two cores). But that's right at the edge, so I'd opt for a 14 AWG cable to have some reserve.
If you can ensure, that you never run at maximum power, you could use a smaller gauge, but I don't think 14 AWG is that massive.
You could also use a fitting cable between the cubes and increase the AWG the further on you get in your chain, so 14 AWG for the first cube, 16 AWG for the next and so on, but I don't really see a benefit there.
And for ease of installation use a stranded wire cable.