Here is a link to a page on the Jaycar website that shows the RGB 4x4x4 cube. Dimensions are not clear or obvious and maybe could be inferred from the size of the LEDs :
Following the link to the Downloads will bring you to this pdf. The construction instructions in the pdf might give a good guide to assembly but they do not detail any form of testing.
Reverse engineering, connectivity test, has shown that even and odd pairs of the LEDs are connected. The 4 LED bars are multi-layer PCBs and it seems the vias are plated through. My simple LED test, anode to cathode with a series limit resistor, does not illuminate each LED separately ...
And by the way, see how other folks recognise the RipOff
XC4498
Colorduino code