Extracting colour out of strawberries
As the comments seem to suggest, making food coloring from strawberries is generally not done because there is not enough red pigment in the strawberries to develop a concentrated red dye. 

Food dyes generally need to be really concentrated to provide the coloration without introducing too much liquid(especially in baked goods). It seems unlikely or at least very impractical to concentrate the pigment enough to be useable as food coloring (unless you want a pale pink). 

In this article, someone makes a dye from strawberries to dye yarn: http://knitting.about.com/od/dyeingyarn/ss/Dyeing-Yarn-With-Strawberries.htm by boiling strawberries and then simmering for 20 minutes. But the concentration of the dye needed to dye yarn is much less than what would be need to dye cake. The dye would introduce way too much liquid in the cake before it can really dye the cake the vibrant red. It seems likely that if you boil down the strawberry liquid enough, you might be able to produce a dye that gives a light pink but nowhere near the bright red that you seem to want.