Preheat the oven to 350°F. Lightly grease (but don't flour) the bottom only of your choice of pan(s): one 9" x 13" pan, two 9" round cake pans, three 8" round pans, or the wells of two muffin tins (24 muffin cups). You can also line the muffin tins with papers, and spray the insides of the papers.
In a large mixing bowl, whisk together the sugar, flour, baking powder, and salt.
Add the butter and beat with an electric mixer at low speed, until the mixture looks sandy.
Combine the milk and vanilla and add, all at once. Mix at low speed for 30 seconds, then increase the speed to medium and beat for 30 seconds.
Scrape the bottom and sides of the mixing bowl.
With the mixer running at low speed, add 1 egg. Increase the speed to medium and beat for 30 seconds.
Repeat this procedure with the second egg. Continue adding the eggs, scraping after each addition, until all 4 are added.
After the last egg is added, scrape the bowl once more, then beat at medium-high speed for 30 more seconds.
Transfer the batter to the pans of your choice. For layers, divide the batter among the pans. Smooth out the tops with an offset spatula or the back of a tablespoon. For cupcakes, scoop by heaping 1/4-cupfuls into the prepared muffin tins.
Bake for 35-40 minutes for a 9" x 13" pan; 30-35 minutes for 9" layers; 24-27 minutes for 8" layers, or 23 to 25 minutes for cupcakes.
The cake is done when it's golden brown around the edges and just beginning to pull away from the edge of the pan. A toothpick inserted in the center will come out clean.
Remove the cake from the oven and allow it to cool for 5 minutes, then turn it out onto a rack to cool completely.
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