What day of the week will be $1993^3$ days from Sunday?

Question

Can anyone show me how to solve this problem in a simple way?

What day of the week will be $1993^3$ days from Sunday?

Here is what I did: $1993^3=7916293657.$ $7916293657$ is divisible by $7$, so the answer should be Sunday. First the answer is wrong, second there must be a better way to solve the problem.

Answer 1

$$1993 \equiv 5 \mod 7$$

$$5^3 \equiv (-2)^3 \equiv -8 \equiv -1 \mod 7$$

Hence, it is a Saturday.