It should be possible, if the subject is given enough time and approaches the task from a rigorous angle, to deduce that the object must be a cube. through a path like...
eyes -> visual processing of the brain -> logical facts about -> mental model of the object in question -> categorizing the mental model -> determining what the object is.
However, I think, the fundamental issue is that in sight, touch etc, typically the concious/logical part of the brain is not involved in determining objects. probably because this is much to slow. There is dedicated hardware/software that does this as far as i am aware.
There are people with the condition where they cannot name, or identify objects from touch but can from sight, even more interesting some people can identify things from touch with their right hand, but not with their left.