Recently, the application of digital cable transmission standards as a second generation digital transmission system for cable systems (DVB-C2) in addition to MPEG-2 video compression has offered ways to provide a variety of digital high definition television (HDTV) programs. In the DVB-C2 system, the use of an orthogonal frequency division multiplexing (OFDM) modulation enables the delivery of innovative video-on-demand (VOD) and HDTV services. In this paper, a computationally-efficientleast-squares estimation of carrier frequency offset and sampling frequency offset is proposed in the OFDM-based DVB-C2 system. To obtain the noise averaging effect in the synchronization process, we adopt a block-by-block correlation, where observation symbols within two correlation blocks are added and the result is correlated. The use of block-by-block correlation improves the estimation performance and relieves the computational overhead. To optimize the performance of the block-by-block estimation method, the mean squared error is theoretically calculated. It is confirmed from simulation results that the performance of the proposed method is enhanced with a low complexity, in comparison with the existing methods.