Japanese 4-in-1For a first time attempt at constructing a juggling cube, I would recommend nothing larger than a 5x5x5 cube. Begin by constructing a 5x5 sheet of Japanese 4-in-1 maille. I would recommend using a relatively small link with a decently thick wire gauge. Alternatively you could simply double up on all the links. A good place to start would be 0.25" ID rings of 16 gauge wire.
Japanese 4-in-1Once 5 of these sheets have been constructed, you are ready to connect them in a three dimensional pattern. Simply use a connecting ring (or rings) on each set of links which sit vertically when the sheets are placed on their sides.
Of course this figure cannot show every connecting ring, but the appropriate connections become obvious once the sheet are created. As with all things, a certain amount of experimentation is required before the perfect combination of wire gauge and links size is obtained.