Content Delivery Networks (CDNs) are a key enabler for geographically-distributed content delivery with high throughput and low latency. As CDNs utilize the underlying optical core network infrastructure, they inherit its vulnerability to targeted link cut attacks which can cause severe service degradation. One of the fundamental problems in CDN configuration is deciding on the placement of content replicas across the underlying network of data centers, which should obtain balance among multiple, often conflicting performance criteria. This paper investigates the implications of minimizing the average distance between the users and the content replicas on the CDN robustness to targeted link cuts.To this end, we compute Pareto-optimal replica placement solutions with minimal user-to-replica distance and maximal robustness to link cut attacks of the highest damaging potential. k-best replica placement solutions in terms of the user-to-replica distance are calculated by formulating the problem as an Integer Linear Programming (ILP) exact method. For each replica placement solution, the worst case link cut attack scenario is identified by defining the Critical Link Set Detection (CLSD) problem. CLSD returns the link set whose cutting disconnects the maximal number of nodes from the content. We develop an ILP model for the CLSD and evaluate the robustness of the resulting CDN attack scenario in terms of mean content accessibility. The approach is evaluated through extensive simulations on real-world reference topologies, indicating that it is possible to improve the robustness to link cuts at the expense of small user-to-replica distance penalties. Moreover, the improvement of robustness is more significant for topologies with smaller average node degree and when cuts involve a larger number of links.