An important mechanism for ice cloud formation in the Earth's atmosphere is homogeneous nucleation of ice in aqueous droplets, and this process is generally assumed to produce hexagonal ice. However, there are some reports that the metastable crystalline phase of ice, cubic ice, may form in the Earth's atmosphere. Here we present laboratory experiments demonstrating that cubic ice forms when micrometre-sized droplets of pure water and aqueous solutions freeze homogeneously at cooling rates approaching those found in the atmosphere. We find that the formation of cubic ice is dominant when droplets freeze at temperatures below 190K, which is in the temperature range relevant for polar stratospheric clouds and clouds in the tropical tropopause region. These results, together with heat transfer calculations, suggest that cubic ice will form in the Earth's atmosphere. If there were a significant fraction of cubic ice in some cold clouds this could increase their water vapour pressure, and modify their microphysics and ice particle size distributions. Under specific conditions this may lead to enhanced dehydration of the tropopause region.