I trust this is one of the most common question when approaching with adding webpart to you sandbox solution through SharePoint 2010 or SharePoint 2013
I have researched google for a while and can't find any solution to reference.
The problem is I can't find any references to SPLimitedWebParManager as well as ListViewWebPart, SummaryLinkWebPart, SPWebPartManager, ContentEditorWebPartand the difference in the DLL: Microsoft.SharePoint. in MS Visual studio 2012.
So Does SP2010 and 2013 not support that API?