As a note I'm answering this question based on avoiding artificial food dyes (Red #40, Yellow #5, etc) rather than all food coloring.
Raspberry puree will produce a pink result, and I have sucessfully done a very dark pink with ground freeze dried raspberries. Achieving the depth of color needed to provide a true red or blue would require not only several food sources to blend the color correctly but a large quantity of, for example reducing juice to make it more concentrated since what you are going for is a color concentrate.
Another option is to let someone else do the blending and extracting for you. Chocolate Craft Colors and a few other companies make plant derived food colorings, and I like the chocolate craft ones since they disclose all of the plant sources (cabbage in the blue, and beets with carrots for the red) and they sell liquid, paste, and powder so you can achieve the color you want without throwing off the balance of the recipe.
To extend what GdD said, the reason why yeast raised breads and quick breads are so different comes down to gluten development.
Yeast raised breads have structure based on gluten, which is a protein created in wheat flours (due to enzymatic action on other proteins in the flour) over time in a moist environment, or when physically agitated. Gluten has a strong, elastic structure providing the toothsome bite typical of yeast raised breads. The techniques, which typically involve one or more of:
- Long, slow fermentation by yeast--the physical raising of the dough not only leavens it, but also helps gluten development
- Kneading, to enhance quicker gluten formation
- So called autolysis, or allowing to set in cool conditions as a moist dough for slow gluten development without extra work from kneading
The result is a strong gluten structure, trapping gas bubbles, giving the charactaristic texture of breads.
Quick breads are the polar opposite. As a general class, they are intended to be tender and soft, not chewy and resilient. The "muffin method" used to create them intentionally minimizes gluten development by:
- Not using yeast to raise the dough
- Mixing a minimal amount to discourage gluten formation
- Baking immediately (in most cases) after the batter is combined, in order to mininize gluten development from sitting time in moist conditions.
The result of course is a tender cake, bread, or muffin.
Typical cake techniques such as the creaming method also control gluten development by:
- Pre-creaming the butter with sugar, and then adding the eggs prior to combining with flour. The fat/sugar phase then coats the flour particles minimizing their interaction, and discouraging gluten formation.
- Cake batters, like quick bread batters, are not usually held, minimizing time for passive gluten formation
Each of these methods is tuned for the outcome desired, and they cannot easily be swapped.
That being said, there are quick breads which are less like the sweet cake like banana bread for example--the most iconic is probably Irish soda bread, but this does not change the general fact that yeast raised breads are a very different beast due to the gluten development. Still, they are their own beast, and not like a yeast raised bread.
Best Answer
Yes, but it's a pain (and depends how much kitchenware you have). When I was in the Peace Corps, I learned how to construct an "oven". You'll need two pots of the same diameter that are big enough to enclose your cake pan, hopefully with about at least an inch of room on all sides. (Just one pot is needed if it's tall enough.)
Put one pot on the burner, then put something in it to elevate the cake pan at least 1/2 inch above the bottom of the pot. Three small rocks work well, as will three stacks of coins. Put the cake pan on top of this stand, then put the last pot upside-down on top as a lid. (If your first pot is tall enough, you would only need a regular lid, not a second pot.) It's best to set this up on the burner as moving it can be risky. Use a low setting for the burner and expect a longer baking time.
This method can work on a stove or on a charcoal grill (with very low heat in the case of grill). It will work better if you can add heat from the top as well (e.g. put a few coals on top). It's finicky though and takes some practice. Bread is a pretty safe thing to try, though I would guess that a box-cake would do okay.
Microwave cake is an easier option, just google "microwave cake" and you'll find lots of recipes.