If the cable box is connected to TV via HDMI (HDTV or digital video signal), then CC inside TV will not work. That's how HDMI works. You have to enable CC via menu setup of cable box ONLY if the cable box supports CC so that CC is overlayed on video signal and transmit CC to the TV. It's almost like sub-titles with DVD/Blu-ray disks.
CC inside TV will work with cable box only if the cable box is connected with composite signals (RCA plugs/jacks) which is analog.
If you use Over-the-Air (OTA) antenna, then CC inside HDTV will work because OTA TV signals are not encrypted. HDTV or digital video signals from cable box is encrypted which is why CC inside TV won't work with external cable box via HDMI cable.
Why? That's the way the idiotic engineers designed them.
Peter