Turn on a multi-functional pressure cooker (such as Instant Pot(R)) and select Saute function. Add sugar and butter to the pot; stir until butter melts, about 5 minutes. Add milk and cocoa powder. Whisk until smooth and starting to bubble, about 5 minutes. Remove pot and let chocolate mixture cool, 5 to 10 minutes.
Pour 1/2 cup chocolate mixture into a small bowl. Reserve for drizzling over the cake.
Whisk eggs, one at a time, into the remaining chocolate mixture in the pot. Add flour and baking soda; mix thoroughly.
Return pot to the cooker. Close and lock lid. Select Cake function according to manufacturer's instructions. Set timer for 30 minutes. Allow 10 to 15 minutes for pressure to build.
Switch to Warm function after timer goes off. Set timer for 30 minutes.
Unlock and remove lid; lift out pot. Run a knife around the sides of the pot to release cake. Place a serving plate on top. Invert cake onto the serving plate.
Poke holes in the cake with a toothpick or sharp knife. Drizzle reserved chocolate mixture slowly over the cake, letting it absorb the chocolate.