For the snake of the shape (- is straight, . is corner)
--...-..-...-.-....-.-.-.--
it prints two solutions. The syntax is borrowed from https://www.jaapsch.net/puzzles/snakecube.htm.
The solutions will also be given using the letters F, L, U, B, R, D standing for the six directions in space where the next cube might be, viz. Front, Left, Up, Back, Right, Down respectively.
winners:
Start: 0,0,0
F F R B U U R D D F U L L B B R D R U U L L F F R R R
Y\X Z0 Z1 Z2
↓→Z →zZ ↓←←
↓Z↓ ↑Zz ↓→z
→↑Z ↑←← →→→
Start: 0,0,0
F F U B R R U L L F R D D B B U L U R R D D F F U U U
Y\X Z0 Z1 Z2
↓Z↓ Z←z →→z
↓↑↓ →→Z ↓←←
Z↑Z ↑zZ →zZ
It also works with any other snake shape and cube size.