Ken's POTW
A Magic Cube
In a 3x3x3 cube, there are 27 unit cubes. Is it possible to put the
numbers 1 through 27 into the cubes such that the sum in any line of
three cubes is the same? If so, show how.
If not,

Can a different set of 27 unique numbers be found to fit the
requirements, or can you prove such a cube cannot be made?

What is the configuration which comes closest to a magic cube (i.e.
all faces are magic squares, or all rows and columns in each direction
have the same sum)?

This is open ended, so please send in any related information.
Source:
Original, with influence from many puzzle sources.
Solution
Mail to Ken