The ultra‐dense low earth orbit (LEO) satellite constellation (UD‐LSC) networks are expected to be incorporated in future wireless networks, particularly 6G networks, to provide global wireless access with enhanced data rates. This paper investigates the downlink multigroup multicast transmission for UD‐LSC networks, in which LEO satellites provide the multicast service for ground users with full frequency reuse. Moreover, in‐network caching, as a key enabling technology of information‐centric networking, is brought into UD‐LSC networks to achieve both bandwidths saving and delay reduction. However, the multicast capacity is constrained by the signal to interference and noise ratio (SINR) of bottleneck users in each multicast group. Besides, the high‐speed movement of LEO satellites makes cache placement and updating more challenging than ground networks with immobile base stations. To track these problems, we first propose a cache‐enabled multi‐satellite cooperation framework and formulate the multicast transmission problem and the content caching problem. Then, to reduce the average content delivery delay (CDD) of ground users, we propose a cooperative multicast beamforming and transmission‐aware dynamic caching (CMB‐TDC) algorithm based on the sample average approach and successive convex approximation. Simulation results show that the proposed CMB‐TDC algorithm can improve the multicast capacity, and then the average CDD is reduced for UD‐LSC networks.