Questions on congruences, linear diophantine equations, greatest common divisor, divisibility, etc.

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$6 \times 6$ and $7 \times 7$ integer matrices

Can one fill a $6 \times 6$ matrix with integers so that the sum of all the numbers in each $3 \times 3$ square equals $2016$ and the sum of all the numbers in each $5 \times 5$ square equals ...