There are only 2048 layers. I used the statistics from [1] at 5:20 from day one.
Layer 1, 66,631,501 cubelets remaining on the current layer and 33,982,651 cubelets destroyed in total. Because it is the first layer it is made up out of 66,631,501 + 66,631,501 = 100,614,152 cubelets. An estimate of the edge length is obtained by dividing by 6 faces and taking the square root and this yields 4,095.0000407. It is a bit counterintuitive - at least for me - but the actual edge length is 4,096. I would have expected that counting the edges twice and the corners trice becomes insignificant for large edge lengths but if you do the math you will see that this approximation has the limit n - 1 as n goes to infinity.
So because every layer adds 2 to the edge length there are 2048 layers. That is bad - there is no central cubelet because the edge length is not odd. Maybe this is the hidden secret. I guess they used 4096 because it simplifies texturing the thing, implementing level of detail or stuff like that, does it? Or they have 8 secrets in there to make it a tiny bit more fair.
One more thing, the number of cubelets on the surface of a cube with edge length n is n^3 - (n - 2)^3 - the whole cube minus the smaller cube under the surface. Plugging in 4096 yields the number obtained from the statistics so we probably made no mistake.
Okay, let's fix the other numbers, too. The cube started with 68,719,476,736 cubelets. I assume the current layer was 263 - the statistics gives the number of layers removed and layer 263 seems to be more consistent with the time of the comment - and there are 23,220,183,736 cubelets in those layers. Subtracting the 17,758,801 cubelets remaining yields 23,202,424,935 cubelets destroyed in 166 days or roughly 139.8 million cubelets per day. There are 45,517,051,801 cubelets remaining and assuming the same rate of destruction this yields roughly 326 days to go.
[1] https://www.youtube.com/watch?v=giEykqDoUCQ