Coded computing has received significant attention thanks to its advantage in alleviating the straggler effect in distributed computation framework, which would be one of the key fundamental techniques to enable the distributed and decentralized network architectures towards 5G-advanced and 6G era. Specifically, considering the scenario that multiple tasks randomly arrive at the network, the additional task queuing makes the delay analysis of coded computing more challenging. In this paper, we consider the impacts of task queuing and characterize the end-to-end delay for coded computing systems under the multi-task scenario. To this end, we first model the end-to-end coded computing system. Then, based on the redundant task processing strategies, we consider both purging and non-purging coded computing schemes. Although the expected end-to-end delay for both schemes are intractable, we obtain closed-form expressions for their respective lower and upper bounds, which generalizes the delay results of the single-task scenario. Moreover, we show that the multi-task coded computing has a coding gain of Θ(log n ) where n denotes the number of worker nodes, even with task queues considered. Simulation results verify the accuracy of the derived delay bounds and show the effectiveness of coded computing in the multi-task scenario.