Of Dumps and Cubes, and Structured Nonsense
Clean, 150 145 143 bytes

Contains many non-printable characters.

import StdEnv
$d=map(\c=['ULFRBD ']!!(digitToInt(['96':d]!!(toInt c))))['&#20;&#27;&#1;&#14;&#30;&#1;&#6;!&#1;&#12;&#24;&#1;B5&#1;J8&#1;P;&#1;H2&#1;)*&#1;\'&amp;&#1;-,&#1;/$&#1;&#21;&#28;&#29;&#1;&#7;&#31; &#1;&#5;"&#23;&#1;&#19;&#25;&#26;&#1;C76&#1;A43&#1;O1&lt;&#1;Q:9']


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Defines the function $, taking [Char], and giving [Char].

This works by mapping each character position in the input to another character position in the output (using the character codes in a string), taking advantage of the swapped 'cubies' in the output being paralleled by swapped colors in the corresponding position in the input.

Output is separated by spaces.