The Successful Search for the Smallest Perfect Magic Cube 
order  exists  disproved or discovered by 
date 
3  no  John Hendricks *  1972 
4  no  Richard Schroeppel  1972 
5  yes  Walter Trump Christian Boyer 
November 2003 
6  yes  Walter Trump  September 2003 
7  yes  Andrew H. Frost  1866 
8  yes  Gustavus Frankenstein  1875 
n>8  Single Solutions were found by several authors  
2k>4  yes  General solution by Mitsutoshi Nakamura 
July 2004 
Three aspects of the nearly perfect magic cube of order 4 Walter Trump  January 2nd, 2004  
The 16 rows, 16 columns, 16 pillars and 24 diagonals are magic (sum = 130). The 4 triagonals have the sums: 100, 120, 140 and 160. Each of the 12 orthogonal planes contains a (nonnormal) magic square. 
The first known perfect magic cube of order 5 Walter Trump and Christian Boyer, 20031113 

This cube consists of all numbers from 1 to 125. The sum of the 5 numbers in each of the 25 rows, 25 columns, 25 pillars, 30 diagonals and 4 triagonals (space diagonals) equals the magic constant 315. 