"On page 26 of the same volume regarding the reforms of Paul I, it is noted that he reorganized the Artillery and Engineer Cadet Corps as the Second Cadet Corps, 'which now gave no special artillery education.'"
Yes, Paul ordered to change the educational program of the Artillery and Engineer Cadet Corps to the same pattern as in the Land Cadet Corps, but he ordered this in the later years of his reign, and the educational program of the Land Cadet Corps also included algebra, geometry, physics (including ballistics) and fortification. Many artillery officers and most commanders of artillery companies graduated from the Artillery and Engineer Cadet Corps before the change had taken its effect. Some artillery officers graduated from the Land Cadet Corps.
"Page 63 of Volume II states that 'in 1800-1806, there was no military educatinal establishment in Russia that provided any special artillery education, except a class in the Guard Artillery.'"
Yes, but in this period any cadet graduated from the First (former Land), or the Second (former Artillery) Cadet Corps, or from the officer class at the Guard artillery was allowed to become an artillery officer by passing an exam at the special commisson.
"The French first founded an artillery school in 1679 at Douai and the French artillery educational system was formalized in 1720. Most of the European artillery advances during the period were French, and the Austrians used the French model when establishing their artillery school in the 1750s."
The Russian artillery educational establishments also had their history starting from the reign of Peter I. By the way, Kutuzov graduated from the Artillery and Engineer School, which later became the Artillery and Engineer Cadet Corps.