We fail to prove this configuration colorable.
We color the boundary nodes with all 27 possible color combinations, modulo equivalence of colors, that are consistent with this smaller configuration:
We see no way to color the configuration given any of the 8 following boundary rings (though other rings, listed below, work):
In case you were interested in the successful parts,
18 successes are simple and 1 requires Kempe-chains.
with color-flipped boundary nodes marked with heavy dashes. (Apologies for the kempe chain edges passing through things visually.)