Which code/class can I use to copy data from an excel datagridview and pasted to a SQL server table (VB)

You cannot 'paste' data to SQL.
You can open SSMS and open a table in Edit mode and then insert data but that is not the correct way of doing it.

Data is inserted into a database table using an INSERT command, which requires a DbConnection object & a DbCommand object.

If using MSSQL these are SqlConnection and SqlCommand objects but there is other DbConnection & DbCommand objects for other database types.

MSDN References for SQL objects are below;
SqlConnection Class (System.Data.SqlClient)[^]
SqlCommand Class (System.Data.SqlClient)[^]
Additional information, including examples, can be accessed below;
Retrieving and Modifying Data in ADO.NET | Microsoft Docs[^]

Kind Regards