The WinServer 2008 Core Edition was the server that you cannot install the SQL Server 2008. The Win Server 2008 Core Edition can run specific server roles such as:
It hasn't the GUI to operate with these roles and, also it doesn't have the .Net Framework which is the reason that the SQL Server 2008 cannot install on it, or at least it is not supported by Microsoft!
The new version of the Win Server 2008 R2 Core Edition can support the installation, but many of the features are required to add them before installation of SQL Server 2008. It can be found at BOL for SQL Server 2008 R2.
The following Features are required for SQL Server database components and those features must be added to Win Server 2008 R2 using OCSETUP :
Important Note: Don't forget that
you shouldn't do these things in Production Servers, it would be better
if you test them in Test Servers environment, yes test test test
... then if you need & if you decide then go for the Production
Server! This note is based on the information for the 64 bit Server
where the Microsoft doesn't support yet (info EEx64