This paper proposes several improved Side-channel cube attacks (SCCAs) on PRESENT-80/128 under single bit leakage model. Assuming the leakage is in the output of round 3 as in previous work, we discover new results of SCCA on PRESENT. Then an enhanced SCCA is proposed to extract key related non-linear equations. 64-bit key for both PRESENT-80 and 128 can be obtained. To mount more effective attack, we utilize the leakage in round 4 and enhance SCCA in two ways. A partitioning scheme is proposed to handle huge polynomials, and an iterative scheme is proposed to extract more key bits. With these enhanced techniques, the master key search space can be reduced to 28 for PRESENT-80 and to 229 for PRESENT-128.