Srr, to ask but whats cured wood ?
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The term "curing" is more regularly referred to as "seasoning" here.
When we cut wood, process it, split it, and stack it, it usually has a moisture content too high for a clean fire. Of course it is wood, and will burn, but it will sputter, boil out moisture (which takes heat away from the process of heating a room for instance), might smoke more, might leave deposits in the flue. Ultimately, letting a stack of firewood season for a time will result in a lower moisture content, and a cleaner more efficient burn.
Now, the part that is debated regularly. I like to let my split wood season (or in your term cure) till the moisture content is below 20%. Some people will sell it before that. Some folks like their wood seasoned even further.
When I cut a standing dead Red Oak, it usually splits at about 38 or 39%, and in the conditions here where I live, it usually loses about 2% of moisture per month. Of course where you stack, how much wind, and sun, and the relative humidity will impact seasoning rates.
I would imagine other folks will provide their own answer.