I’ve been meaning to write a more detailed post about this for a while, and it looks like somebody beat me to it! There’s a video on YouTube with 69,000+ views, which acknowledges that it got its inspiration from a cake on Reddit, but doesn’t mention *who* on Reddit made that cake. That would be me.
I did, in fact, make a separate batch of batter for each color. Any time you’re making a 10” round cake (in straight-sided pans), you’re going to need a full box of cake mix for each layer, so since I made three separate 10” rounds - 3 boxes of cake mix.
Yes, I use cake mix. (Duncan Hines. Always Duncan Hines.) I used to bake from scratch, when I went through my “I MUST MAKE EVERYTHING MYSELF AND IT MUST BE ALLLLLLL NATURAL” phase (after the birth of my first child, stereotypically enough) - but I kept on overhearing comments about how my cakes had a “weird” texture. Americans like their cakes so soft that they’re practically falling apart, it seems. So I started using doctored cake mixes. In general - follow the directions on the box, but add 1 extra egg and an envelope of either pudding mix or Dream Whip.

(This is your best friend if you’d prefer that your cakes not fall apart as you ice them. Image Source: Amazon.com)
For the white cake, I used WASC (White Almond Sour Cream - or in this case, WSC, as I left out the almond extract), which is a very popular recipe in cake decorating communities. I always add Dream Whip to this, too; and I use pure vanilla instead of clear. It doesn’t make all THAT much of a difference in the color, but it does affect the taste.
For the blue, I used Betty Crocker’s Blue Velvet recipe. I’m going to be honest with you, though - I didn’t like how it tasted. If I ever do this again, I think I’ll just add the blue dye to WASC.
(Sure does look pretty, though, doesn’t it? Image Source: BettyCrocker.com)
I bought some Betty Crocker gel food coloring at the grocery store, because I knew it was going to take a lot of blue dye, and I didn’t want to waste my precious Americolor. I used the entire tube, and still had to use some Americolor Royal Blue. Also, it’s very, very important to add some Violet, or else the blue will just not look right.

(This. This is what happens when you don’t add Violet.)
I did try to do the stars, too. I figured I’d do it like a Funfetti cake - I even ordered a bottle of all-white sprinkles. It didn’t work…you can’t see them in the finished cake. White baking chips might work better, but I haven’t tried that yet, so YMMV.
For the red I used Red Velvet. It takes so freaking much dye to get a decent shade of red, that it would be quite pointless to try to dye white batter red. Don’t waste your time, your red dye, or your sanity. Just use Red Velvet. (Protip: use chocolate pudding mix with this one.)

(This is what your sink will look like while the mixing bowls soak. There will be red and blue splatters everywhere…just, everywhere.)
When baking anything larger than 8”, I always set the oven to 325. Not 350. Low and slow is the way to go for larger cakes - if you bake them hot & fast, the edges will burn before the center is done. That’s also how you get cakes that are domed in the center. (Another trick is to use an upside-down flower nail as a heating core in the middle of the pan.)
So. Now we have three 10” rounds: one red, one white, and one blue.

(Not pictured: white. Obviously. You can see the tips of the flower nails peeking through the centers of the cakes.)
It’s time to start slicing!
I used my trusty cake leveler and started torting (slicing) the red and white layers. I had figured out exactly how thick the layers needed to be in order to get all 13 stripes - I think it was 1/4”. So I started out slicing them super thin, but I got nervous about how flimsy that first layer was, so I moved the wire up a notch. (You can see that the bottom white layer is thinner than the rest of them.) Because of this, I ran out of cake and couldn’t make it to 13. Bummer.

(Look upon my shame.)
Once I had the red and white layers stacked up (with as little frosting between layers as possible), I cut a 4” circle in the middle of the top three layers, and removed the outer ring.

(How did I know how deep to cut? I’m just that good.)
I then removed a 4” circle from the middle of the blue cake, and put the blue ring together with the red and white center. It cracked as I was assembling it, unfortunately. I did my best to patch it up with a cake scrap, but it showed through in the finished cake as a pretty sizable dent. Fondant is incredibly unforgiving of flaws in the cake, unlike buttercream, which can be molded pretty much however you want it.

(I was paranoid about making sure the blue cake was thick enough, so I didn’t level it until after all of the pieces were together.)
After that, it was just frost, cover, decorate! I used fondant, but like I said, fondant is ridiculously unforgiving. A cake with so much going on inside is very likely to have some dents and dips and cracks and general imperfections, which are much easier to cover up with buttercream. (It doesn’t matter how smooth you get your crumb coat - the fondant WILL sink into the holes. It just will.)
I don’t have any progress pics of the decorating itself - I was panicking too hard about the massive dent to even think about picking up my camera. (Seriously, I considered submitting it to Cake Wrecks as a Missed Mark.) I covered the whole cake in white fondant, and used my circle cutter to cut the concentric circles for the top. I used my ribbon cutter for the pieces on the sides. I have a nesting set of star cutters that I got from the 100¥ store, which came in very handy for this party.
My recipes/process for the buttercream and fondant deserve their own entries. So to conclude, I’ll leave you with another picture of my adorable little JD:

The last picture I posted hit it big on Reddit. Some really nice things have been said.
There were a couple of requests for more pictures, so here’s what I have. I didn’t take as many progress pics as I would have liked, because the process was a bit messier than I was expecting. (Crumbs and frosting ERRRRRVRYWHERE!) I also didn’t take too many (good) pictures of the outside of the cake, since it came out a bit lumpier than I would have liked.
I threw in a picture of the other cake I made on JD’s actual birthday, just because I think he’s adorable. Carry on.