We study age of information in multi-hop multi-cast cache-enabled networks where the inter-update times on the links are not necessarily exponentially distributed. We focus on the set of non-arithmetic distributions for inter-update times, which includes continuous probability distributions as a subset. We first characterize instantaneous age of information at each node for arbitrary networks. We then explicate the recursive equations for instantaneous age of information in multi-hop networks and derive closed form expressions for expected age of information at an end-user. We show that expected age in multi-hop networks exhibits an additive structure. Further, we show that the expected age at each user is directly proportional to the variance of inter-update times at all links between a user and the source. We expect the analysis in this work to help alleviate the over-dependence on Poisson processes for future work in age of information.