Iphone charger keeps cutting in out when charging.

I recently bought a brand new lightning to usb charging cable. Since I got the charger and plugged it in for the first time i've been noticing an issue where it will intermittenly cut in out and without me moving the cord or even touching my phone, this happens about every 5 minutes. I tried to clean inside my charging port to see if that was the problem but it didn't work and I even tried cleaning the gold pins on the tip of the charger that plugs into the actual phone because I did notice some carbon build up. I even tried changing the brick to see if that would help with the problem. I also tried plugging the charger into other devices and the problem persisted, so I know that something is deffinetely wrong with the charger it self. Is there anything else that I could try doing that could fix this problem?