When you say cloud database, do you mean SQL Azure? If so, Azure SQL does not support replication.
If your cloud database is a full copy of SQL Server (i.e. not express), you can set up transactional publishing with renewable subscriptions or use merge publishing. Both options allow you to synchronize changes in any database.
Edit
To clarify, you can use SQL Server Express for replication, but only as a subscriber. The publisher must be a Workgroup editor or higher.
source share