1. A memory system comprising: a first memory including a plurality of blocks, each of the plurality of blocks being a data erasing unit and including a plurality of pages, each of the plurality of pages being a data writing unit and capable of storing a plurality of clusters; a second memory configured to temporarily store data read out from the first memory; and a controller configured to write data stored in the second memory to one or more of the data writing units of the first memory and manage a storage position of the data in the first memory, wherein the first memory includes a management information storage region that stores management information indicating the storage position of the data in the first memory, and when the controller writes update data in the second memory to the first memory and a difference between a size of the page and a size of the update data is equal to or greater than a size of the cluster, the controller configured to: generate write data by adding, to the update data, data which has the size of the cluster; store an update content of the management information corresponding to the update data and an update content storage position indicating a storage position of the update content of the management information in the first memory; and write the generated write data to a block in writing of the first memory.