Smallest Seventh Power which is Sum of 8 other Seventh Powers

Theorem
The smallest seventh power that can be expressed as the sum of $8$ other seventh powers is $102^7$:
 * $102^7 = 12^7 + 35^7 + 53^7 + 58^7 + 64^7 + 83^7 + 85^7 + 90^7$