An active material composition includes a porous graphene nanocage and a source material. The source material may be a sulfur material. The source material may be an anodic material. A lithium-sulfur battery is provided that includes a cathode, an anode, a lithium salt, and an electrolyte, where the cathode of the lithium-sulfur battery includes a porous graphene nanocage and a sulfur material and at least a portion of the sulfur material is entrapped within the porous graphene nanocage. Also provided is a lithium-air battery that includes a cathode, an anode, a lithium salt, and an electrolyte, where the cathode includes a porous graphene nanocage and where the cathode may be free of a cathodic metal catalyst.