All six faces of the cube are formed with the same blocks of 2x2 tangle
All eight corners of the cube are formed with the same L-block; all the quarter-circles are oriented around the corners of the cube, thus the figure has 8 'contracted' circles.
Rather than using the original alphabetical labels of the tangle pieces, I have identified each piece with a number 01 - 24, each one appearing four times.
Solutions 3,4 and 6 have one axis of symetry marked with a cross, thus
the cube is formed of two identical halves;
solutions 1 and 5 have three axis of symetry, thus the cube is formed of four identical 'bicubic' blocks;
solution 2 has no axis of symetry but it is in a certain sense mirror-symetrical.
In the six solutions, the quarter-circles are not always oriented in the same way; thus not all the solutions have the same number of circles: solution 1 has 6 face-circles, 12 edge-circles and 8 contracted corner-circles (the maximum number of circles); solution 2 has only 12 edge-circles; the other solutions have 6 face-circles and 8 contracted circles.
Solutions 3,4,5,6 form a sort of subfamily; for example the 12 tangle pieces of the first L-block around the red corner-circle are exactly the same for these solutions; some of the other L-blocks are the same or are different between the solutions of this family.