The specific heat of water is 4182 Joules/kg and its density is close to 1kg/litre, so 4.128 kJ (Energy) will be required to heat 1 litre of water by 1 degree C.

The temperature rise of the oceans will be complicated to work out. Taking the OPs figures, 4.16x10^14 watts / 1.3x10^21 litres gives 3.2x10^-7 watts per litre of ocean, ie 0.32 microJoules of energy added to the oceans every second. The temperature rise of the oceans will depend on how quickly it can dissipate this heat. What are relevant the heat loss mechanisms? Evaporation just moves the problem to the atmosphere. Conduction just moves it elsewhere on earth. Radiation will shift some of it to space (and some reflected back to the earth), but radiation is a property of the surface of the ocean, not of the bulk.

Amount of energy consumed from global data centers: 205 terawatt-hours. [0]

Amount of water in the oceans: 1,386,000,000 (km3)~= 1.386*10^21kg[1]

water has a specific heat capacity of: 4,200 J/kg°C [2]

Energy/HeatCapacity/AmountOfWater = 1.268×10^-7 degrees Celsius

[0]: https://energyinnovation.org/2020/03/17/how-much-energy-do-d... [1]: https://www.usgs.gov/special-topic/water-science-school/scie... [2]: https://www.bbc.co.uk/bitesize/guides/z2gjtv4/revision/5

You're confusing power and energy here.

Giving OP's number for the volume of water in the ocean, heating the ocean 0.01 K would be 5.4 * 10^22 J. Assuming 365 days in a year, that's 1.7 * 10^15 W, an order of magnitude less than OPs figure for datacenter power-usage.

You mean the figure that OP first increased by 4 orders of magnitude, right?

1 calorie is by definition the energy requires to heat 1 gram of water 1°C. In practice 1ml.

So ~1kcal to heat 1 liter of water 1°C

1 kcal is ~1.163 watt-hours.

That would mean going from 8.4 million data centers to 840 billion data centers. I mean, come on...

But hey, let's roll with it. What would be the effect on the environment if we literally had 10,000 times more data centers ABOVE ground, for comparison? After all, you are neglecting to take into account the fact that a HUGE amount of the wattage used by existing data centers has been cooling via HVAC, and by switching to underwater cooling their overall watt usage would theoretically drop a good bit due to the efficiency gains.

Also assuming we have coated the oceans with a perfect thermal insulator. Otherwise this heat would also radiate away, a small fraction going to the atmosphere and a lot of it back into space.

Watt is a measure of power not energy. Did you mean Watt-hour? The specific heat of water is about 4.2 kJ/kg/K. One joule is one watt for one second, that is 1 J = 1 W.s. So one W for one hour (3600 seconds) is 3.6 kJ and is enough to raise the temperature of a kg of water by about 0.9 K

You need to brush up on dimensional analysis :-)

Unfortunately, the living parts of oceans are also the parts that tend to be easy to get to, and putting stuff farther away will be more expensive. But careful placement may be able to mitigate that.

It is still ultimately a 3D environment where the vast, vast bulk of the 3D environment is not thriving with heat-sensitive life. Our 2D surface intuition misleads us here. Our mental images of the ocean are of the exceptional locations, not the common ones.