I made a cake today using bog standard marge, white sugar, eggs, self-raising flour and a pinch of baking powder. I added enough pink food colour (supermarket brand that comes in the tiny bottles) to make it look dark pink to red. It baked perfectly but lost the pink colour although it did look a bit more golden that it would have done if the colourant was not in it. The date on the bottle was "best before November 2019".
As @GdD has said, a lot of the liquid dyes sold in the baking aisles of supermarkets while adequate for icing etc, are not really designed for baking. If you are intending to bake with a colouring, the powdered food dyes used in Indian and Chinese cooking can produce very deep colours, but they are nearly always synthetic and have been linked to some food allergies. The post What makes food dyes heat-safe? explains more about heat tolerant dyes and lists some good alternatives.