Yes and NoYou cannot add sockets to or remove sockets from an item that already has sockets, but you can add sockets to unsocketed items.There are two main ways to socket white items: the Horodric cube, and Larzuk's quest reward. Both require unsocketed items. The Horodric Cube recipes only work for non-superior items, which makes superior items with less than max sockets valuable, if they have the correct number for a popular item.Socketing Items at LarzukLarzuk is occasionally, if infrequently, a good choice for socketing a white item. An item with sockets has exactly that many sockets forever, and it cannot be altered.You can give white items to Larzuk in Act 5 once per difficulty as a quest reward in order to have him add sockets to the item. The number of sockets added is based on the specific item you're adding sockets to (it will always get the maximum for an item of that type). If you add sockets to a colored item this way, you will get fewer sockets. Most colored items only give 1 socket, although blue (magic) items will randomly give 1 or 2 sockets.
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Once an item has sockets, you can not add additional sockets, or remove any. However, if you have a white item (armor or weapon with no sockets in it), you can add a random amount of sockets to it via Horadric Cube recipes. As bummzack pointed out below, the odds for getting a certain amount of slots via recipe isn't always equally distributed.
The game rolls a random number from 1-6 to determine how many sockets will be added, but if for example the item you have can only have a maximum of 3 sockets, there is a 1/6 chance of adding 1 socket, 1/6 chance of adding 2 sockets, and a 4/6 chance of adding 3 sockets (rolling anything from 3-6 will result in 3 sockets).You can also use your Act 5 Quest 1 reward at Larzuk to add slots. The number of slots added will vary depending on the type of your item. Magic Item ( Blue) = Random 1 or 2 slots. Rare Item ( Yellow) = 1 Slot. Set Item ( Green) = 1 Slot. Unique Item ( Gold) = 1 Slot.
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Normal/Exceptional/Elite Item ( White) = Max # Slots item allows for (not always 6, varies by quality and item type so look this up before socketing!).Note that in your case, only the white quality above matters as you can only put Runewords in white items.