Do there exist natural numbers $a, b, c, d$ such that $a^{3}+b^{3}+c^{3}+d^{3}=100^{100}$?
For example $\left(100^{33}\right)^{3}+\left(2 \cdot 100^{33}\right)^{3}+\left(3 \cdot 100^{33}\right)^{3}+\left(4 \cdot 100^{33}\right)^{3}=\left(1^{3}+2^{3}+3^{3}+4^{3}\right) \cdot 100^{99}=100 \cdot 100^{99}=100^{100}$.

## Answer

There are.