What is the requirment and why are you wanting to create a web-part inside  a web-part. Web-part is a single component that can host multiple user controls and you can achieve what you want.

But there is nothing like creating a web-part within a web-part.

Are you asking about web parts inside  a subsite?

i am very very new to sharepoint just been a month ,there is no requirement right now i was just wondering whether we can thats why i asked.

No you can't create a web-part within another webpart  and this is true for any ASP.net application.

Although you can inherit or extend the non-sealed web parts.

It would be great if you brief what is sealed webpart.
And how to inherit or extend the sealed webpart.

Any links/pointers to the related information would be great.

"Sealed" is a C/C++/C# thing for classes that cannot be inherited or extended.
Web parts are also just like another class and hence any class that is SEALED you can't inherit or extend it.

Web-part is a single component that can host multiple user controls and you can achieve what you want. ...

Actually i am a newbie to Sharepoint... so, can you elaborate the above definition... as i understood only a lill of it. can you please, tell us wat a web part is ... in detail?

A web part is an ASP.NET server control which is added to a Web Part Zone on Web Part Pages by users at run time. Web Parts are an integrated set of controls for creating Web sites that enable end users to modify the content, appearance, and behavior of Web pages directly from a browser. The Web Parts control set is a group of components that work together to enable developers to create Web pages where users can modify the user interface (UI) directly from a browser. The UI controls all derive from the Part class, and they compose the primary UI on a Web Parts page.

Web Parts can be used as add-on ASP.NET technology to Windows SharePoint Services.

More information here: msdn.microsoft.com/en-us/library/e0s9t4ck.aspx

What is the difference between a website and a portal? Are they not the one and the same?