This is a variation on Magrim\'s version, with one correction to the center core symmetry and four added block to the outer shell of layers 1, 3, 4, and 6.
http://imgur.com/gAOL5AD
While it doesn\'t look symmetrical, it helps if you view the center 2x2 of each layer as a 2x6x2 unit by itself. Its symmetry becomes clear. Then you can see that the outer rings of layers 1 and 4, 2 and 5, and 3 and 6 are the same, with 1/4 being mirror images of 3/6.
Odd, but it works.
It\'s possible that shifting the central 2x6x2 column up or down a few blocks could change the output for the better, but I haven\'t tested all alignments yet.
Edit: Nope: Shifting the center core up and down is just creating the same shapes as already exist in the various layers, so if you build the center core first, then arrange the outer rings around it, it won\'t matter how they line up. It should still work.