Due to the fact that network connectivity has a fixed value for a given network, only using network connectivity to improve the survivability of data center networks will reach bottleneck. The content connectivity, which is defined as the reachability of content from any point of a network becomes research focus. In this letter, the definition of k-node (edge) content connectivity is given. Theoretical analysis shows that achieving k-node (edge) content connectivity is equivalent to searching k independent end-to-content paths. Designing k-node (edge) content connected optical data center networks is formulated as an integer liner program (ILP) with objective of minimizing the total wavelengths consumption. Numerical results show that, to achieve dual-node (edge) content connectivity, leveraging content distributed deployment can reduce about 30% wavelengths consumption with NSFNet and about 25% with COST239, than merely relying on network connectivity. Furthermore, about 30% wavelengths consumption could be saved in COST239 to achieve three-node (edge) content connectivity. Data center's storage capacity and location have significant impact on the total wavelengths consumption.