Almost the same as Yuval's answer, except...

If I gave you two 1025 x 1025 matrices, you wouldn't extend them to 2048 x 2048. You'd extend them to 1026 x 1026, and use one layer of Strassen's algorithm with 513 x 513 matrices - if you decided that this is faster than direct calculation of a 1025 x 1025 product. One recursion level lower, you'd decide whether your seven 513 x 513 products are faster to calculate directly or as a 514 x 514 product using one layer of Strassen's algorithm and so on.

I very much doubt that Strassen's algorithm will be an improvement for 65 x 65 products. There are fewer floating-point operations, but probably a lot more overhead.

Almost the same as Yuval's answer, except...

If I gave you two 1025 x 1025 matrices, you wouldn't extend them to 2048 x 2048. You'd extend them to 1026 x 1026, and use one layer of Strassen's algorithm with 513 x 513 matrices - if you decided that this is faster than direct calculation of a 1025 x 1025 product. One recursion level lower, you'd decide whether your seven 513 x 513 products are faster to calculate directly or as a 514 x 514 product using one layer of Strassen's algorithm and so on.

I very much doubt that Strassen's algorithm will be an improvement for 65 x 65 products. There are fewer floating-point operations, but probably a lot more overhead.

For non-square matrices: If you want to multiply a (100x100) by a (1000x100) matrix, that can be done trivially by calculating ten (100x100) x (100x100) products. Filling up to 1000x1000 would be madness.