BIg Rubik's Cube

we have to only count the number of cubes , that are colored from outside . For a 2 x 2 cube , there is no middle or inner cube which is uncolored . In a 3 x 3 cube , there is only 1 inner cube which is uncolored .

Now, we know that only the upper layer of any side of cube is colored whose size is 1 unit. So, when we subtract the side length of 1 unit from both the opposite sides from all the faces of the cube , we get the side length of inner uncolored cube = n - 1 - 1 = n - 2.

So, the volume of uncolored cubes = $(n-2)^{3}$ And the whole volume of the cube is $n^{3}$ .

Therefore, volume or number of uncolored cubes is = $n^{3}$ - $(n-2)^{3}$

In our case , n = 2511.

So finally we get the number of uncolored cubes as $2511^{3}$ - $(2511-2)^{3}$ = 37800602

So, our answer is $\boxed{602}$ .

There always 8 corner cubes, regardless of the size of the rubix cube.

The number of edge cubes not including corner cubes is 12 x (2511-2) because there are 12 edges and there will be 2511-2 cubes per edge.

The number of side cubes not including edge or corner cubes will be 6 x $(2511-2)^{2}$ because there are 6 faces.

Therefore the total number of cubes will be:

8 + (12 x (2511-2)) + (6 x $(2511-2)^{2})$ = 37800602

So the last three digits are $\boxed{602}$ .

For n^3 cube there are n^3-(n-2)^3 small cubes. So the answer is the last three digits of 2511^3-2509^3. Thus the answer is 602.

(2511^2) 6-(2511 12)+8=ans