Driven by numerous emerging services and applications of mobile devices, multi-access edge computing (MEC) is regarded as a promising technique for massive Internet of Things (IoT) with 6G mobile networks to alleviate core network congestion and reduce service latency. However, the conventional MEC suffers from the infrastructure without the cloud server (CS) and cooperation of multiple edge servers (ESs), which cannot deal with the large-scale computation tasks in the ultra-dense smart environments. This paper investigates the issue of the cooperative computation offloading for MEC in the 6G era. The proposed MEC system allows the cooperation of edge-cloud and the cooperation of edge-edge to address the limitation of single ES and the nonuniform distribution of computation task arrival among multiple ESs. To support low-latency services, we model the cooperative computation offloading problem as a Markov decision process, and propose two intelligent computation offloading algorithms based on Soft Actor Critic (SAC), i.e., centralized SAC offloading and decentralized SAC offloading. Evaluation results show that the proposed algorithms outperform the existing computation offloading algorithms in terms of service latency.