The Snake Cube Thingie

Number the cubelets from 1-27, starting from the end that has a 3-cubelet segment followed by a 2-cubelet segment. Here, then, is the location of the cubelets in the finished cube (and 1-27 is the order in which they need to be put in place):

   27  8 21
   26  7 22
   25 24 23

   12  9 20
   13  6 17
   14 15 16

   11 10 19
    4  5 18
    3  2  1