Energy efficient noise dampening coaxial and twisted pair cables include certain layers to improve the quality of signals transmitted over the cables. A coaxial cable includes a conductive core, a first insulating layer surrounding the conductive core, a metal shield layer surrounding the first insulating layer, a second insulating layer surrounding the metal shield layer, a carbon material layer surrounding the second insulating layer, and a protective sheath wrapping the carbon material layer. A twisted pair cable section includes a core section. The core section includes a carbon material core, an insulating layer surrounding the carbon material core, and a metal shield layer surrounding the insulating layer. A plurality of twisted pair cables are disposed in sections or compartments defined by the core section, and between the core section and a protective sheath. Methods for constructing the cables are also disclosed.