I'm reading Cox "Primes of the form $x^2+ny^2$". And I read a chapter about the global m-th power reciprocity law. Now I'm not able to prove the quartic and cubic reciprocity laws. Where can i find the proofs of them using global m-th power reciprocity law. There is a link to Hasse's book "Bericht uber neuere Untersuchungen und Probleme as der Theorie def algebraischen Zahlkorper" in Cox's book. But I haven't found English translation of it. Any recommendations for such books or articles would be of great utility.

@Dietrich Burde I read the chapter about Cubic and Quartic Reciprocity laws a long time ago, and I knew these proofs, but I don't know they could be proved using $m$-th power reciprocity law. I didn't find this law in the book. Speaking about $m$-th power reciprocity law I mean this $K$ is a number field containing a primitive $n$-th root of unity, and $\alpha, \beta \in \mathcal O_K$ are relatively prime to each other and to $n$. Then

$$\biggl(\frac{\alpha}{\beta}\biggr)_{n} \biggl(\frac{\beta}{\alpha}\biggr)_{n}^{-1}=\prod_{\mathfrak p \mid n\infty}\biggl(\frac{\alpha,\beta}{\mathfrak p}\biggr)_{n},$$

where $\biggl(\frac{\alpha,\beta}{\mathfrak p}\biggr)_{n}$ is the $n$-th power Hilbert symbol. Bibliography seems to be quite usefull, i'm going to check it, thanks for it.