The blue corn moon referred to in the song "Colors of the Wind" from "Pocahontas" is a fictitious concept and does not refer to any particular moon phase. The concepts of blue moon and full corn moon do exist and refer to different types of full moons occurring at various times of the year.
According to astrophysicists at NASA, a blue moon is a full moon that occurs a second time within a calendar month. A full moon usually occurs once every 28 days per the normal cycle of the moon. When a full moon occurs between the first and third of a month, there will be another full moon within the same month, occurring 28 days later between the 29th and 31st. This will be the blue moon.
According the Farmers' Almanac, a full corn moon, or full harvest moon, occurs in September and sometimes early October. It is usually attributed to Native Americans because they often harvested corn during this time. The full corn moon rises close to the autumn equinox and marks the time for gathering winter stores. Because this moon provided a bright light well into the night, it allowed for more harvest time. The harvesting of fields cleared the landscape for easier hunting and the collecting of meats for winter storage.
The Cherokee Indians, who resided in North and South Carolina, referred to the July full moon as a green corn moon, signifying corn that had not ripened.