Two aspects have to looked into when using a thermoelectric device to cool something in this manner.
Firstly, the energy load been presented. Using some of the parameters mentioned, like 6 cubic feet (170 litre) volume with 20 l of water, ignoring thermal ingress from the outside. External ambient temperature is 30°C. Internal is a fridge environment
That amount of air weighs about 191 grams which needs 192.6 joules of energy per degree of temperature change; the 20 litre of water weighs about 20 kg which needs 83740 joules of energy per degree of temperature change. The combined energy load per degree is about 83,930 joules per degree.
Using a 12 V power supply,the 12706 device at 35°C (hot side) draws 5 amps (12 volts by 5 amps = 60 watts) (heat flux); this device can transfer about 20 joules per second (going by the data sheets and the cold side would be at -10°C). At that rate, it'll take about 4200 seconds to cool that volume by 1°C. The total hot side heat load will be 21 + 60 = 81 watts. Also, remember no allowance has been made for thermal ingress. ("We're gonna need a bigger boat." :) )
Next aspect is, the hot side temperature and the heat sink dissipation. As the hotter this side is, the less heat that will be moved from the cool side. If the hot side is at 35°C (for the above conditions) a large heat-sink and fan assembly in the 0.06 degrees per watt range would be a good choice (for just one device). This would keep the device about 5°C above the ambient of 30°C.
A more efficient configuration running 2 (or more) of those devices on a 3 amp supply would each transfer about 13 watts (joules per second). So for 26 watts of cooling only 45 watts is used instead of 60 watts with the single device. (This is going into the COP of the device) From the Data sheet, at 3 A, a device temperature differential of 40°C occurs. Fridge internal temperature is about 3 degrees normally. A heat sink for each device is (3 - -5) = 8°C per 13 watts or 0.61 degrees per watt (should be readily available). Also, good volume fans as well as would be required. Alternatively, using a larger condenser plate may achieve the same effect.
Using multiple devices can lower the overall ohmic waste heat load and achieve higher heat transfer. If the devices is supplied with 2 amps, the ohmic heat is 10 watts with 6 watts transferred. If four devices were used at this current, then there is 40 watts of waste heat used to pump out 24 watts of heat. External heat sink rated at 0.315 °C/W, internal heat sink at 1.33 °C/W. Probably need four more to compensate for external heat ingress and fan heat.
For this device, a current of 1 amp will not produce enough device temperature differential to meet the initial requirements.
A good thermostat controlled temperature controller would be a good thing too, if it is a power controller then it may apply a wider range of power the devices to more closely control the internal temperature. But, when all is said and done, for a lot of running time, the cooler only needs to compensate to heat ingress, for the size unit hopefully less than 20 Watts. The time to cool an item is dependent on how many more cooling devices are added and that determines how much power is drawn in that cooling period. Those extra devices won't be running once the desired temperature is reached.
To handle the thermal ingress issue, probably a test and measure method would be the best, but if you assume 20 watts like a previous author then that is simply two more of these cooling assemblies. Although, a 120 cm fan may introduce a 2.5 watt heat load and may be considered for increased air circulation but would decrease the available heat pump capacity. Or you may want the devices on all the time but running at a reduced power to compensate for heat ingress.
But, from an insulation viewpoint and heat ingress, if the 100mm thick polystyrene sheet foam insulation is used then for the 170 liter internal volume, the expected energy required to offset the leakage is 16 Watts. The surface area of a cuboid to contain that volume is 1.84 square meters. You just have to specify the thermal conductance of your insulating material in Watts per square meter per degree and its thickness. (Can you get that information from the AliExpress people on that product?)
To compare with a 170 liter fridge using a compressor/refrigerant, that consumes 150 watts (from what I could find). That could mean 15 of the 2 amp units, producing 90 watts of cooling and bring the initial cooling time figure from 66.61 minutes to nearly 16 minutes. But physically mounting that many devices maybe problematic.
But, if you wanted just one device, use something like a 12740, using 30 amps (ohmic waste heat of 360 watts) generating a cooling effect of 150 watts needing 510 watts dissipated by the external heat sink whilst maintaining the hot side at 50°C. Two of these could make a nice little room heater.
Did you notice that I was referring to current? Well, the data sheets give the performance graphs for a constant current. Those graphs highlight that when the temperature differential is lower that more cooling occurs; meaning that the cooling performance can be much greater when the fridge is "warmer". So, initially, a 4 device configuration of 12706 will have at 2 amp will be about 105 Watts and a waste heat of 36 Watts. Only as the temperature differential increases does the cooling effect lessen. So, the better performing the heat sink is the quicker the cooling; water cooled external heat sink/radiator? Just a thought
Also, the air will cool much faster than the 20 l mass for a number of reasons. The air will be mobile and hence coming in contact with the cold surfaces and will take about 3 minutes to cool down from 30 °C. However, 20 l of water will take more than a day to chill. A 750 ml bottle of wine chills in about an hour
I hope that this helps.