Rubic cube's face into date

[jasen 4]

Solve this rubic cube's face into date

 

[Logophobic 9]

Spoiler

Convert the numbers to base six:

21/05/2013 >> 33/05/13153
16/09/1980 >> 24/13/13100

Place these numbers in the grids, note how they match the color pattern:

3 3 0
5 1 3
1 5 3

2 4 1
3 1 3
1 0 0

Fill in the third grid accordingly:

4 2 2
0 1 1
2 5 1

Take the base-six numbers from this grid and convert to base ten:

42/20/11251 >> 26/12/1615