The Summer Olympics have been cancelled due to war three times: in 1916, 1940, and 1944.
The 1916 Games were scheduled for Berlin but were abandoned because of World War I. The 1940 Games were first awarded to Tokyo, then moved to Helsinki as war expanded in East Asia and Europe; they were ultimately cancelled because of World War II. The 1944 Games, planned for London, were also lost to the Second World War.
This count refers to cancelled Summer Games, not every Olympic event affected by conflict. The 1940 and 1944 Winter Olympics were cancelled too, but they do not add to the Summer Olympics total. The modern Games also experienced postponement in 2020 because of COVID-19, but that edition was held in Tokyo in 2021 rather than cancelled.
After the wartime gap, London hosted the 1948 Games—the only Summer Olympics held during the 1940s.