Each post in a different color

You would have to target each post using the unique ID in the HTML - use inspect element to find the ID of each post.

For example:

.post-1403 .inside-article {
      background-color: #1E72BD;
      color: #FFFFFF;
}

.post-1403 .inside-article a,
.post-1403 .inside-article a:visited {
      color: #FFFFFF;
}

.post-1403 .inside-article a:hover {
      color: #EFEFEF;
}

You can also target post formats, like this:

.format-standard .inside-article {
      background-color: #1E72BD;
      color: #FFFFFF;
}

.format-standard .inside-article a,
.format-standard .inside-article a:visited {
      color: #FFFFFF;
}

.format-standard .inside-article a:hover {
      color: #EFEFEF;
}

.format-quote .inside-article {
      background-color: #181B21;
      color: #FFFFFF;
}

.format-quote .inside-article a,
.format-quote .inside-article a:visited {
      color: #FFFFFF;
}

.format-quote .inside-article a:hover {
      color: #EFEFEF;
}

And where can I use it? I tried to add your example with the help of plugin Simple Custom CSS and it is not working. I need some kind of add-on?

Adding it to Simple Custom CSS should work.

Did you change the post ID to one of your posts? Or did you use the post format examples?