Battery Balancing system
For lithium-ion cells like you're planning to use, no, you will not need multiple cell balancing circuits for each set of parallel cells.  The recommended configuration for lithium-ion batteries is to connect each cell group in parallel first, and then string these parallel groups in series.  Within the parallel group, cells will self-balance.  Each group can basically be treated as one large cell.  

If for some reason you were to construct serial strings of cells first, and then parallel the whole string, then yes, each string would need its own balance circuit, but this is not advised.  

From Battery University:


  With Li-ion, the parallel strings are always made first; the completed parallel units are then placed in series. Li-ion is a voltage based system that lends itself well for parallel formation. Combining several cells into a parallel and then adding the units serially reduces complexity in terms of voltages control for pack protection.