Convolutions on the sphere are useful in many geophysical fluid dynamics problems, and many unstructured numerical methods make heavy use of them. However, when discretized, these convolutions result in sums that scale as O(N^2) in the number of grid points, which is challenging for scaling to large problem sizes. This work will present the Cubed Sphere Fast Multipole Method, a fast summation technique that allows us to approximate such spherical convolutions while reducing the complexity from O(N^2) to O(N). The Cubed Sphere Fast Multipole Method is suitable for a wide range of problems that arise in geophysical fluid dynamics, including tidal simulations and vorticity dynamics on the sphere.