Ultramagic squares of order 7
Walter Trump did some extensive researches with ultramagic squares and found all 20 190 684 ultramagic squares of order 7. You can read his remarks and see his results on his web pages.
One of these ultramagic squares he found is this symmetrical square, which has an inlaid diamond and another inlaid magic square of order 3 with magic sum S_{3}=75.
27  46  31  1  6  17  47  8  9  20  26  34  43  35  29  28  11  32  37  36  2  45  38  40  25  10  12  5  48  14  13  18  39  22  21  15  7  16  24  30  41  42  3  33  44  49  19  4  23 


27  46  31  1  6  17  47  8  9  20  26  34  43  35  29  28  11  32  37  36  2  45  38  40  25  10  12  5  48  14  13  18  39  22  21  15  7  16  24  30  41  42  3  33  44  49  19  4  23 

You can also find some other interesting ultramagic squares like this one, which is bimagic and trimagic in the diagonals. The magic sums are S_{7}^{2}=5867 and S_{7}^{3}=221 275.
1  7  46  44  33  34  10 
41  24  39  27  18  5  21 
31  13  12  8  36  28  47 
30  48  15  25  35  2  20 
3  22  14  42  38  37  19 
29  45  32  23  11  26  9 
40  16  17  6  4  43  49 