Sprinkles are nothing but starch, sugar, and food coloring pressed into pellets.
When sugar or starch gets wet, like from batter, it will eventually dissolve, especially when it gets heated up.
If you want the sprinkles that don't dissolve when they get wet or heated up in baking, then you will need to get what is called "pearls". The proper name for them is Dragees I think. They are like little shiny balls, sort of look like metal balls or pearls. They come in different sizes and colors. But again, these ARE made of sugar and starch and can dissolve, but usually take a lot longer to dissolve than the other types.
If you want sprinkles in your cake, it is going to be difficult for any sprinkle NOT to dissolve to some extent while baking. The harder the sprinkle, the less likely it is to dissolve quickly.
I would suggest, if you want solid color shapes in your cake, use something like M&M's or chopped up hard candy of some kind.
The BEST way to use sprinkles in a cake, is to mix them in at the very last second before you pour the batter into the pan and stick it in the oven. The less time it has to sit in wet batter, the better off you will be.
You might try MY method.........
1. Lightly butter or grease the bottom of the baking pan (you just want enough for the sprinkles to stick)
2. Scatter your sprinkles all over the bottom of the pan.
3. Pour 1/2 of the batter into the pan, smooth it over the bottom of the pan covering the sprinkles.
4. Scatter more sprinkles over the cake batter in the pan.
5. Pour over the remaining batter over everything and smooth over.
6. You can scatter more sprinkles if you want over the top, but be sure and lightly run the spatula over them so they get covered with a bit of batter, otherwise they usually burn.
Bake the cake.
Your sprinkles shouldn't dissolve as fast this way, as you aren't mixing them into the batter, but kind of layering them into the batter in the pan.....they shouldn't dissolve as quickly and hopefully have more time to not bleed out into the cake, so you get more bits of solid color. But there are no guarantees.
Hope that helps.