The roll-out of various emerging wireless services has triggered the need for the sixth-generation (6G) wireless networks to provide functions of target sensing, intelligent computing and information communication over the same radio spectrum. In this paper, we provide a unified framework integrating sensing, computing, and communication to optimize limited system resource for 6G wireless networks. In particular, two typical joint beamforming design algorithms are derived based on multi-objective optimization problems (MOOP) with the goals of the weighted overall performance maximization and the total transmit power minimization, respectively. Extensive simulation results validate the effectiveness of the proposed algorithms. Moreover, the impacts of key system parameters are revealed to provide useful insights for the design of integrated sensing, computing, and communication (ISCC).