Meanwhile, heat the olive oil in a large pot or Dutch oven over medium heat.
Add the garlic and cook, stirring occasionally, until golden, about 3 minutes.
Add the clams, wine, corn kernels and cobs, red pepper flakes and 1/2 teaspoon salt; cover, increase the heat to high and cook until the clams open, about 7 minutes.
Discard the corn cobs and any unopened clams.
Add the butter, lemon zest and pasta to the pot with the clams; toss to coat, about 1 minute.
Add some of the reserved pasta cooking water to loosen the sauce if the pasta seems dry.
Stir in the parsley and season with salt and pepper.