inspiredby.brand.com is still a good option and is a subdomain, but if you can use inspiredbybrand.com, it will be better.
inspired.brad.com means something different, semantically speaking, so you should try to avoid that. One idea is that something is inspired by the brand and the other is that the brand is inspired, be careful.
The word "by" is a stop word. This means that more probably than not it'll be ignored by Google and the other Search Engines. So, you won't really get a more seo-friendly URL and your users will be bored by those useless extra characters to type and remember. In conclusion, go ahead with inspired.brand.com. In addition, a good thing you can do is set the title meta-tag of the page to "Inspired by Brand".