The indentation response of Nickel nano double gyroid films has been measured using a Berkovich nanoindenter and the effective mechanical properties of the Ni double gyroid lattices inferred via a multi-scale finite element analysis. The 1μm thick double gyroid films were manufactured by block copolymer self-assembly followed by electrodeposition of the Ni resulting in two interpenetrating single gyroids of opposite chirality, an overall relative density of 38% and a cell size of about 45 nm. The measured hardness was ∼0.6 GPa with no discernable indentation size effect. A multi-scale finite element (FE) analysis revealed that the uniaxial compressive strength is approximately equal to the hardness for this compressible lattice. Thus, the 38% relative density Ni double gyroid has a strength equal to or greater than the strongest fully dense bulk Ni alloys. The FE calculations revealed that this was a consequence of that fact that the Ni in the 13 nm gyroid struts was essentially dislocation free and had a strength of about 5.7 GPa, i.e. approaching the theoretical strength value of Ni. The measurements and calculations reported here suggest that in spite of the nano gyroids having a bending-dominated topology they attain strengths higher than those reported for stretching-dominated micron scale lattice materials made via 3D printing. We thus argue that relatively fast and easy self-assembly processes are a competitive alternative to 3D printing manufacture methods for making high strength lattice materials.