I have cadets interested in taking private pilot lessons through our squadron with a CAP Instructor Pilot and in our CAP aircraft. What costs are the cadets responsible for?

None except for examiner fees for issuance of an FAA pilot certificate or rating.  Charges and fees are covered in CAPR 70-1.

The cadet may be required to pay for the use of the aircraft; however the wing/unit/other members may opt to pay the fees associated with flying for the cadet. Some wings have cadet flight scholarships. The cadet should contact unit officers first to see how funding works in their unit/wing.