This is embarrassing. Got so distracted with the other things you got wrong, I didn't check the basic maths. As far as I can make out, your calculation, even if it wasn't simplistic and rather irrelevant, is out by multiple orders of magnitude.
Looks like you've converted 1.73×10¹⁷ Joules (energy) to kcal, which gives your figure of about 4×10¹³ kcal (energy), but the value is 1.73×10¹⁷
Watts (power), which is Joules
per second. Don't know where you got the year from. The link you had for your 173,000 TW wording was misleading because it referred to it as energy, but it did say "strikes the Earth
continuously" (not per year), which was a clue. I guess it was due to the fact it was about solar power, and in the generation business, they tend to talk about 'energy' in Megawatts, rather than 'power', which is what they mean.
en.wikipedia.org
"
For example, the heat required to raise the temperature of 1 kg of water by 1 K is 4184 joules, so the specific heat capacity of water is 4184 J⋅kg⁻¹⋅K⁻¹."
Sticking with sensible units and taking the figure you gave for the power delivered by the sun, of 1.73×10¹⁷ W or J⋅s⁻¹, and the volume of the oceans you also gave of 1.4×10¹⁷ L. Take a nominal density of water to be 1 kg⋅L⁻¹, we need 4184 J for each litre of water, which will be 4184 × 1.4×10¹⁷ = 5.86×10²⁰ Joules to raise the temperature of the oceans by 1 K. We are getting 1.73×10¹⁷ J each second, so it will take 5.86×10²⁰ ÷ 1.73×10¹⁷ = 3387 s. That's about 56.4 minutes. So for 1.5 K (°C), we have about 85 minutes or 1 hour 25 minutes.
This agrees with this online water heating calculator:
Use the water heating calculator to determine how much time and energy you'll need to increase the temperature of the water.
www.omnicalculator.com
Of course, sending all the sun's radiation to heat to oceans is absurd, but it shows that the temperature increase over years is trivial considering the amount of heat arriving (and leaving) the earth each second.