With properly designed assembly jugs
"jugs"?
Big jugs are always good. Whenever you can get away with it, stick BRA 0xDD somewhere in your code! However in this case s/jugs/jugs/
Built on veroboard of course!
I've only made a 4x4 cube bit it was almost impossible to get 16 slightly misaligned LED legs inserted into veroboard. 10x10? Never going to happen.
(I believe they use foam at the bottom of LED cubes for this reason...)
No problem - you've got 10 separate vertical 10x10 planes to fit and if built on a jig the spacing will be pretty accurate. Each only has 10 wires to solder to the veroboard at the bottom of the cube.
Solder the 10 common anode wires straight across all the planes at the back of the cube, then add 10 vertical wires with a right angle bend at the tip to clear the horizontal wires, staircase fashion to connect them down to the veroboard.
100 wires of ribbon cable with the ends fanned out to the individual cathode column pads + 10 heavier wires for the common anodes soldered trackside to go off to the driver board