Preheat the oven to 350F/176 C. In a medium bowl sift or whisk together the flour, salt, dry instant vanilla pudding mix, and baking powder.
In a separate large bowl add the eggs and vanilla extract. Beat the eggs with a mixer. Then add the softened room temperature butter and sugar. Cream those ingredients together with the mixer. Scrape the sides of the bowl as necessary.
Now add half of the milk and half of the flour mixture in with the batter. Mix those in. Then add the rest of the milk and the rest of the flour and mix completing the batter.
In a medium bowl add the hot water and cocoa powdered. Mix those together until the cocoa powder is dissolved. Then add a little less than half of the vanilla cake mix to this bowl. Mix to combine, creating the chocolate cake portion of the marble cake.
Grease a 9x5 inch bread pan with butter or shortening and then dust it with flour. Next spoon in some vanilla cake batter, then some chocolate cake batter on top of that. Now do another layer of vanilla and then chocolate, etc. Alternate between layers until all the cake batter is gone. Use a knife or wooden skewer and draw an s pattern in the cake. This will help create that cool marble look.
Bake the cake on the middle rack of the oven for 45 to 55 minutes until a toothpick comes out clean. Allow the cake too cool for 15 minutes once out of the oven. Then remove the cake from the pan and allow it to cool on a wire rack completely. Cut into it and enjoy it! Store it in an airtight container or ziplock bag at room temp or in the fridge.