Permutations of $9\times 9$ Sudoku square Strang 2.1.35

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The question concerns a $9\times9$ sudoku square.

The question is what exchanges of rows will produce another valid $9\times9$ sudoku square. I understand that rearranging the rows in each block of $3$ rows will produce a valid $9\times 9$ sudoku square and there are $6$ such permutations of the three rows.

He then calculates the total number of permuted $9\times 9$ sudoku squares to be $6^4$.

I do not understand why this is has to be to the power of $4$? Given that there are $3$ blocks of $3$ lines I would expect the answer to be $6^3$ (where $3$ refers to the number of blocks?)

Where have I gone wrong?