packing uniform cuboids into regular cube I have a pile of uniform cuboids, of side a,b,c. I would like to make a regular cube. The sides are not in harmonic ratio ( cf. de Bruijn) but are in fact white sugar lumps.
The minimum regular cube I can envisage is of side a+b+c. 
I have experimented making a 3x3x3 cube of 27 cuboids using a 3x3x3 magic cube to direct operations but find that 


*

*I get a non tight pack on 2 out of 3 levels

*I cannot make a 3rd level that is compatible with the first two, one cuboid has to be omitted from the arrangement.


It seems more likely that I should be using a 6x6x6 magic cube formulation to match the 6 orientations of the cuboids a.b, b.a, a.c, c.a, b.c, c.b. But while I can visualise a 3x3x3 I would need to know how to encode the cells of a published 6x6x6 cube into these 6 possible cuboid orientations.
Any thoughts are appreciated

so it is obvious that I cannot get a tight pack, any one face of slice of the cube must have a 'hole' in it, so restricting to one 2D section
laid out as a magic square 
ABC
CAB
BCA
where e.g. A is a cuboid laid down with its b and c edges face down, and so occupying a footprint of b*c
the length of a side is a+b+c, the overall area is (a+b+c)^2
but the component cuboids will present a total area
3ab+3ac+3bc
and the difference not be equated to zero
(a+b+c)^2 - 3ab+3ac+3bc = 0
except in the case a=b=c
