The Rubik's Cube's properties

One of the most popular puzzles

worldwide, the Rubik's Cube, was 

designed by Hungarian architect Erno 

Rubik. 

The cube consists of 27 individual cubes, 

arranged in a 3x3x3 order, and each 'face', 

or 3-by-3 square, can be rotated, to 'shuffle'
the cube. Once shuffled, it is the goal of
the 'cubist' to get it back to the original position.

Now, the notation. If you put the cube in front
of you, then the side facing you is called 'front',
obviously. As follows, the side directly above
it, is called 'up', the side to the right is 'right', the
side to the left is called 'left', the bottom-most side
is called 'down'. And the side opposite 'front' is
called 'back'. It's unlikely that this side will be used.

The moves are such that if the command is 'front',
(F) for example, I would turn that face once, clockwise.
If the command is 'down inverted' (D') , I would rotated
the down side once, counter clockwise. If the command
is '2 up' (2U) , then I would rotate the topmost side twice, in any
direction.

Now, what I wanted to talk about- the algorithms. These are
a fixed set of moves, which will enable a cubist to perform a
desired function on the cube, without disrupting what has
already been performed. But an algorithm can be any set of
moves. What I want to consider is the number of times an
algorithm takes to come back to its original state. I'll call this its
Cube-Length. The Cube-Length will be more in the 3x3x3.

Algorithm                                 Cube-Length

R (One right turn)                             4 (Times to loop back)

2R                                                   2

U, R (Up, then Right)                       15

U, R, F                                            12

U, R, F, L                                         9