The Hypercube Doubling Theorem  

Given any semi magic latin order m hypercube ^{n}L_{m} distributed
over the order 2 hypercube ^{n}T_{2} which after changing digits turns into an "augmentation" magic latin hypercube of order 2m ^{n}A_{2m} = ^{n}T_{2}(^{n}L_{m}) = m^{n} (D(F_{i,j}(^{n}L_{m}))  1) (i,j = (0,1)) To this augmentation hypercube any order n hypercube can be added to each hyperquadrant such that ^{n}H_{2m} = ^{n}A_{2m} + G_{i,j}(^{n}H_{m}) is a regular magic hypercube 

Distribution functions F_{i,j}() and G_{i,j}() 
The distribution functions where in the original method mirroring in the central horizontal and vertical. In order to obtain an order 4 form the order 2 I found G_{i,j}() need also to include a center mirroring (NEED TO VERIFY) 

latin hypercube ^{n}L_{m} 
Regularly the used hypercube is a zero nagonal order m hypercube (need checking, possibly more general possibilities!?) 

Digit changing D_{i,j}() 
Changing digits in the distributed latin hypercube is needed to compensate the offsums in the obtained order 2m square. Off sums (+c) in one hyperquadrant need to be compensated into an adjecent hyperquadrant by a factor (c) thus forming the hyperquadrants compenstion patterns (++) or (++) for squares and (++++) or (++++) for cubes. The encyclopedias database lists the data for the order 2 and 3 square and cube, and a derivation method to obtain data for other orders and dimensions as well. 

Augmentation hypercube ^{n}A_{2m} 
Multiplying the above obtained square by m^{n} an augmentation hypercube is obtained to which any order m hypercube can be added, a little care is needed in the choise of the distribution function G_{i,j}() to avoid doubly appearing numbers 