310.15 B2a
"(2) Adjustment Factors.
(a) More Than Three Current-Carrying Conductors in a Raceway or Cable. Where the number of current-carrying conductors in a raceway or cable exceeds three, or where
single conductors or multiconductor cables are stacked or bundled longer than 600 mm (24 in.) without maintaining spacing and are not installed in raceways, the allowable
ampacity of each conductor shall be reduced as shown in Table 310.15(B)(2)(a)."

"240.4 Protection of Conductors. Conductors, other than flexible cords, flexible cables, and fixture wires, shall be protected against overcurrent in accordance with their ampacities"

Sorry if the cut & paste produced a lousy format job but these are quotes from the 2002 NEC.

The important part of the first one is "the allowable ampacity of each conductor". That means the ampacity after all derating factors are applied. That's just like trying to put a 60A breaker on a #14 THHN. The allowable ampacity of #14 is only 15A.