Why do we need to go through multiple cycles in block cipher
First of all, I wouldn't rely on that book for information about modern cryptography.  It might be a fine reference for networking in general, however based on the example they gave, it would appear that they really don't know their crypto.  The example cipher they gave feels like something from the '90s.

Modern block ciphers use $k=128$; the issue with $k=32$ is that you tend to leak information about the plaintext after encrypting a few gigabytes with the same key; with modern networks, you can hit a few gigabytes easily.  In addition, key dependent sboxes have gone out of fashion; they are a bit expensive in hardware, they tend to leak timing data in software (due to caching), and the sboxes are sometimes not particularly strong against differential or linear cryptanalysis.

As for your question:


  Why do we need to process the text through n such cycles?


Consider the case where $n=1$, and you have two different plaintexts that differ in a single bit.  Then, if you look at the two parallel encryptions, the inputs for seven of the sboxes are precisely the same (because they only depend on inputs that have not changed), and so only one sbox (say, $T_0$) has its output changed.  That sbox has 8 output bits, and so when you go through the 64-bit scrambler, then you have 56 output bits that would always be the same, and 8 that are potentially changed.  This is far short of 'any input bit can potentially affect any output bit'.

There are more sophisticated things we can do for larger $n$; this simple reasoning shows that the $n=1$ case just doesn't cut it...