Is there any permission required to built similar style of (Stackoverflow)? I reviewed both: http://creativecommons.org/licenses/by-sa/3.0/ and https://blog.stackoverflow.com/2009/06/attribution-required/ but they not mentioned Website Style?
From the legal page:
The Network and its contents are intended solely for the use of the Network Subscribers and may only be used in accordance with the terms of this Agreement. All materials displayed or performed on the Network, including, but not limited to text, graphics, logos, tools, photographs, images, illustrations, software or source code, audio and video, and animations (collectively, “Content”) (other than Content posted by Subscriber (“Subscriber Content”)) are the property of Stack Exchange and/or third parties and are protected by United States and international copyright laws.
So, no, you can't use the styles in your design.