Sounds like the signal is Macrovision-protected.
If there's a way to turn off "auto level control" for video recording on the VCR (not likely), do that and it will work. Otherwise, the only way is to put a low-pass filter on the video wire between the cable box and the VCR.
Most VCRs adjust the brightness as they record to get a better picture. Macrovision puts a burst of white in the signal between frames -- where it won't show up on a TV -- to confuse a VCR into recording black. Turning off auto level control makes the VCR ignore this, but very few if any VCRs can do this. A low-pass filter cuts off the signal when it gets too high, so it lets everything but the bright burst through, letting your VCR record normally.
Joe McKenzie, July 2007