Will the series 6 band fit series 3

I cannot say this from my experience, but I think it will not work.

This article said:

"The Solo Loop and Braided Solo Loop bands are designed specifically for Apple Watch Series 4, Apple Watch Series 5, Apple Watch SE, and Apple Watch Series 6."

Also, on the product page if you check the compatibility list it shows:

Yes.

38mm Series 3 can use the new 40mm band

42mm Series 3 can use the new 44mm band.

Note: You have 14 days return window if it's not suitable.