The essential book for family historians is Cumbrian Ancestors 4th edition (2014) published by and available from Cumbria Archive Service.
Also Cumberland and Westmorland: a genealogical bibliography. Stuart Raymond. 1993. Published Federation of Family History Societies - ISBN 1 872094 56 2.
Cumberland books can be searched in the LDS FamilySearch Catalog to find those available on-line, in FamilySearch centres, or in the Library in Salt Lake City.
Much useful information can be found in Cumbria FHS Publications including many transcriptions for the 1851 census. There is an index to Newsletters.
The Cumberland and Westmorland Archaeological and Antiquarian Society (CWAAS) has listing of its publications and its invaluable Transactions. These latter can be downloaded by CWAAS members (those older than 5 years for non-members). Printed Transactions are held by several public libraries within Cumbria and elsewhere.
Google Books and Internet Archive (Open library) have thousands of digitised books with "Cumberland" in the title or text.