I want a 'simple' proof to show that:

$$1^4+2^4+...+n^4=\frac{n(n+1)(2n+1)(3n^2+3n-1)}{30}$$

I tried to prove it like the others but I can't and now I really need the proof. Also I want a **geometric proof** for that and this one below:

$$1^3+2^3+3^3+...=(\frac{n(n+1)}{2})^2$$

**geometric proof**: I want a proof using shapes and geometry.