This is how I think it works. We've got this situation:
The great grandparents are first cousins, meaning they share a set of grandparents. They are expected to share about 900 cM with each other, and each of the segments that make up that 900 cM come to both of them from one of their grandparents:
So the great grandparents each get one full chromosome of 3600 cM from the unrelated parents, and they were passed 2700 cM from their related parent that the other didn't get, and they get 900 cM from their related parent that are the same segments that the other was passed.
They pass 1/2 of their DNA to their children, 1/4 to their grandchildren, and 1/8 to their great grandchildren who are the 2nd cousins.
So there is a 1/8 chance that each 2nd cousin gets one particular segment, meaning there is a 1/8 x 1/8 = 1/64 chance that each 2nd cousin gets the same segment.
From the diagram above, you can see that the great grandparents have in total 3600 x 4 = 14,400 cM. If they did not share any segment, then the 2nd cousins would be expected on average to get 14,400 x 1/64 = 225 cM.
But they do share DNA. They share 900 cM. What that means is that if one 2nd cousin got a piece of that shared DNA from either grandparent, and the other got the same piece from either grandparents, then the 2nd cousins would share that segment. The Most Recent Common Ancestor (MRCA) in this case would not be one of the great grandparents, but it would be one of the great-great-great grandparents.
Since the 2nd cousins can get that piece from either great grandparent, there are therefore 4 possible ways the two of them could get the segment. Both from GGP1, Both from GGP2, One from GGP1 and the other from GGP2, One from GGP2 and the other from GGP1.
This means there is 4 times the chance of the 2nd cousins both getting DNA from the 900 cM shared between their great grandparents than there is from anywhere else.
So the 2nd cousins are therefore expected to share in the unshared great-grandparent region:
(3,600 + 2700 + 2700 + 3600) x 1/64 = 196.875 cM
And they'd share in the shared great-grandparent region:
900 x 1/64 x 4 times the chance = 56.25 cM
The total expected shared is 196.875 + 56.25 = 253.125 cM
This is 28.125 cM or 12.5% more than the expected amount of 225 cM.