How can I create multi columns from a single unordered list?

I'd like to create a multi column list like this: https://jsfiddle.net/37dfwf4u/

No problem when using a different list for each column:

<ul>
    <li>item1</li>
    <li>item2</li>
    <li>item3</li>
    <li>item4</li>
</ul>
<ul>
    <li>item5</li>
    <li>item6</li>
    <li>item7</li>
    <li>item8</li>
</ul>

ul {
    display:inline-block;
}

However, can this be done by a continuous list and pure CSS so that the CSS arranges the columns automatically? E.g. by use of flex layout which I'm not yet familiar with?

Yes, you can create a multi column list as described if you make the ul a flex container, change the flex-direction to column, allow it to wrap by applying flex-wrap: wrap and additionally force it to wrap by limiting its height:

ul {
  height: 100px;
  display: flex;
  flex-direction: column;
  flex-wrap: wrap;
}

<ul>
  <li>item 1</li>
  <li>item 2</li>
  <li>item 3</li>
  <li>item 4</li>
  <li>item 5</li>
  <li>item 6</li>
  <li>item 7</li>
  <li>item 8</li>
  <li>item 9</li>
  <li>item 10</li>
  <li>item 11</li>
  <li>item 12</li>
  <li>item 13</li>
  <li>item 14</li>
  <li>item 15</li>
  <li>item 16</li>
  <li>item 17</li>
  <li>item 18 </li>
  <li>item 19</li>
  <li>item 20</li>
  <li>item 21</li>
</ul>

Here's another possibility, added half a year later after the comment by @Andrew Koper:

You can also use the colummn-count parameter, which doesn't require a fixed height (and also not flex), but defines a fixed number of columns. So in the example below, even just two list items would be broken into two columns of one list item each:

ul {
  column-count: 2;
}

<ul>
  <li>item 1</li>
  <li>item 2</li>
  <li>item 3</li>
  <li>item 4</li>
  <li>item 5</li>
  <li>item 6</li>
  <li>item 7</li>
  <li>item 8</li>
  <li>item 9</li>
  <li>item 10</li>
  <li>item 11</li>
  <li>item 12</li>
  <li>item 13</li>
  <li>item 14</li>
  <li>item 15</li>
  <li>item 16</li>
  <li>item 17</li>
  <li>item 18 </li>
  <li>item 19</li>
  <li>item 20</li>
  <li>item 21</li>
</ul>

Consider using CSS3 Multi-column Layout for that:

CSS3 Multiple Columns

You can do that using just one list and define the number of columns with CSS. If you check CSS3 Multi-column layout browser support here you can see partial support by most of the browsers, because they do not support break-before, break-after and break-inside properties. But they do support the properties you will need to create a multi column list with a prefix.

.container {
  -webkit-column-count: 2; /* Chrome, Safari, Opera */
  -moz-column-count: 2; /* Firefox */
  column-count: 2;
}

ul {
  margin: 0;
}

<div class="container">
  <ul>
    <li>item1</li>
    <li>item2</li>
    <li>item3</li>
    <li>item4</li>
    <li>item5</li>
    <li>item6</li>
    <li>item7</li>
    <li>item8</li>
  </ul>
</div>