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Solve this rubic cube's face into date

enter image description here

For puzzle masters who can not see pictures / color blind

B B W
Y G B  = 21/05/2013
G Y B 

R O G
B G B  = 16/09/1980
G W W

O R R
W G G  =  ?
R Y G
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A Rubik's cube has six faces, so there are six different colors to work with.

This suggests to me that it's

a base-6 encoding, where each color corresponds to a number from 0-5.

Sanity check: in base 6, a 2-digit number can represent up to 35 in base 10, so 2 digits will be enough for the month and day in base 6. That leaves 5 digits for the year, which can represent up to 7775 base 10. So it's an appropriate number of digits.

So I changed each of the dates into

Base 6 representation.
21/05/2013 becomes 33/05/13153
16/09/1980 becomes 24/13/13100
Then I looked at the pattern of the color blocks.

These patterns fit:
330513153 matches the pattern BBWYGBGYB from the first block;
241313100 matches the pattern ROGBGBGWW from the 2nd block.

Thus the colors represent:

Digits: White = 0, Green = 1, Red = 2, Blue = 3, Orange = 4, Yellow = 5.

Read the pattern from the 3rd block:

ORRWGGRYG = 422011251
Day (base 6) = 42
Month (base 6) = 20
Year (base 6) = 11251
42/20/11251 converted to base 10 is 26/12/1615

So my answer is:

December 26, 1615

I'm not sure the significance of this day, if there is one.

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