Generalized Magic Objects

Lets a Generalized Magic Object of order n be defined as:
nG-Magic Object {f(xi)|g()}
n: The order of the object
with: G = IC, IR, IQ, IZ, IN
Object: Square, Cube, Tesseract ....
f(): number generating function
g(): 'magic condition'

The regular magic squares can be defined in terms of the above as
nIN-Magic Squares {f(i) = i (i = 1..n2)|'sums' = magic number}
The p MultiMagic squares can be defined in terms of the above as
nIN-Magic Squares {f(i) = ik (i = 1..n2; k = 1..p)|'sums' = magic number}
in the above examples 'sums' means of course all sums horizontally, vertically,
and along both diagonals
(the above defines p seperate magic squares)