That sort of error can occur if you have more than one face sharing the same space. I'm betting that, in order to create this multi-sided, multi-faced cube, you copied one side and pasted it in a new location, perhaps after (or before) rotating it. I'll bet you actually have more than one copy laying on top of another.
A word to the wise: renderer's don't really know what to do with polygons that occupy the same space. You and I may normally perceive this as merging or combining surfaces. Unfortunately, render engines don't really "think" like you and I.
You can confirm my suspicions by calculating the total number of faces you SHOULD have, and compare this to the actual number of faces Anim8or says you have (Options > Info). My quick calculation says you should have (7 x 7 x 6 x 6 =) 1764 faces. I'll bet Anim8or claims you've got more.