Let's count.

Fix the blue side of the cube to be on top.

The 2 reds can be

1 on bottom and 1 on the side.

1 on the side and the next adjacent to it.

1 on the side and 1 opposite it.

The greens fill up all the other sides.

All other possibilities can be rotated to one of these.

So there are 3 distinct cubes.