Nearly 147 flat teaspoons.
Sugar, or sucrose, is soluble and therefore will dissolve in any liquid.
The amount that can be added before it stops dissolving depends on when the liquid becomes “saturated” – the point at which no more solvent can be dissolved and either remains as a solid or is let off as gas.
In the case of sugar this would be the point at which the sugar settles on the bottom of the cup.
For this article we are basing our calculations on six US fluid ounces (177.44ml).
It is worth noting here that the temperature of the water has an effect on the saturation point and therefore the result will differ between a hot and cold cup of tea.
This is not the rate at which the sugar dissolves (which is faster in hotter liquids because of the increased energy) but the point at which the liquid becomes saturated which is higher in hotter liquids.
We will assume the sugar is somehow added very quickly to the tea shortly after the water is boiled and therefore say it is at a constant 90C, despite this being somewhat unrealistic.
Hardcore sugar fans will be familiar with the classic book A Handbook of Sugar Analysis, in which Dr C A Browne shows the solubility of sugar at 90C is 415.7g per 100ml.
We can therefore calculate that our cup of tea will dissolve 737.62g (415.7 x 1.7744) of sugar.
To put that into perspective this is equivalent to 184.4 sugar cubes or 146.8 level Imperial teaspoons (5.91939047ml teaspoon x the weight of 1ml of sugar which is 0.849g).
Pass the sugar.