Is there a sudoku (Latin Square Pattern) state in a Rubik's cube $6\times6\times6?$

Solution 1:

Yes, there is such a state.

At least http://www.randelshofer.ch/rubik/vcube6/X900.01.html claims to present two sequences of moves that each will create one.

Here they are (but I'm not sure how to read the notation):

Algorithm Michael Z. R. Gottlieb 2008
F R' B' D2 · F' B2 · D2 L D' F R' F' U' F' R' B R U2 TF TR' TB' TD2 · TF' TB2 · TD2 TL TD' TF TR' TF' TU' TF' TR' TB TR TU2 T3B T3L T3U2 T3B2 T3L' T3B T3U T3L' T3U2 T3L' T3B' (47 btm)

First

Second

Final

Algorithm Walter Randelshofer 2014
U SF SR SD' F2 SR2 B U SF2 D2 WR2 U WR2 TU S2F S2R S2D' TF2 S2R2 TB TU S2F2 TD2 M2R2 TU M2R2 T3U2 T3B T3L2 T3U' T3L2 T3U T3B2 T3L' (34 btm)