Disconnect the inner cable from the brake calliper and then hold the cable taut where it was connected to the brake. Pull the brake lever and then release it while still pulling on the cable. This will tell you if the cable is sticking or not. If it is sticking, the first thing to check is the outer cable ends as when these are cut they can collapse inwards which in effect restricts the inner cable movement. If the cut ends of the outer are perfectly round that can be excluded as the cause. If the cable is still sticking, I would then remove it from the outer and check the entire length. If no faults found reinsert into the outer but ensure it is well oiled as you insert it. If doing this has not revealed a problem, check the brake calliper. Squeeze both brake blocks in towards the rim and then release. When squeezing inwards there should be a good amount of resistance and as soon as you release it the caliper should spring back away from the rim. If it does not do this, the calliper may be dirty and need cleaning and re lubing or the spring could be damaged or not correctly located.