How many 6-input LUTs are necessary to synthesize any 10-variable switching function?
In the 8-variable case, you need a 256-bit LUT. So you distribute that over four 64-bit LUTs, and use a fifth LUT as a 4:1 multiplexer to select the correct output.

So, for 10 variables, you need 16 of your 64-bit LUTs, and a 16:1 multiplexer, which requires 5 more LUTs.

You can also think of it as four copies of your 8-variable circuit (20 LUTs), with one more 4:1 mux to select the correct output from them.