Cubozoans are rare as fossils.
A few probable cubozoans are known as fossils from the famous Mazon Creek locality (Pennsylvanian age) near Chicago, Illinois. One of these fossils, Anthracomedusa turnbulli, is shown to the right in a somewhat squashed condition; the bell is towards the top, and three bunches of tentacles can be seen at the bottom. Other fossils from the same locality more clearly reveal the square shape and four bunches of tentacles, features that indicate Anthracomedusa was very likely a cubozoan. A few other fossils that may be cubozoans have been found in the Jurassic Solnhofen Limestone of Bavaria, Germany.
One Vendian fossil, known as Kimberella, was thought to be a cubozoan, but re-study of numerous specimens from the White Sea region of Russia has shown that Kimberella is unlikely to have been a box jellyfish.
Sources:Fedonkin, Misha A. and Waggoner, Benjamin M. 1997. The Late Precambrian fossil Kimberella is a mollusc-like bilaterian organism. Nature 388(6645): 868-871.
Foster, Merrill W. 1979. Soft-bodied coelenterates in the Pennsylvanian of Illinois. pp. 191-267 In: Mazon Creek fossils. edited by Nitecki, Matthew H. Academic Press, New York, NY.