The chromatic numbers of queen− n2 graphs are difficult to determine when n > 9 and n is a multiple of 2 or 3. In previous works [6, 7], we have proven that this number (denoted χn) is equal to n for n∈{12,14,15,16,18,20,21,22,24,28,32} and that χ10=11. This article describes how, by extending slightly further the previous work, the chromatic number of queen− 262 and queen− 302 can be obtained. A more general result, proving that χ2n=2n and χ3n=3n for infinitely many values of n, is then presented.