Burn on wood floor repair

Hello,
I have a burn the size of a flood light bulb (4"-5" diameter circle) on a wood floor. The floor is a relativley cheap pine wood floor. The burn is deep sanding will not take it out. I was thinking about sanding the area and filling with Bix Stain Putty. Does anyone have any experience with repairing a deep burn on a wood floor?

Thank you!
Sean

mmm
the only way is to pull up the board and replace the burnt section
radical but it will be ok
after a while the new section will blend in

filling with putty will always look crap and by the time you are done puttying, sanding, tryi to make it blend in you may as well have pulled the board and replaced it - it will be quicker