Interspersed between my Endeavor Entries, I've put it upon myself to use all that I have at my fingertips to unravel what is already known and what is assumed about Slenderman, the Rake and all that still remains unseen. This will be more analysis
What does Slenderman feed on? Does he need nourishment? Quite frankly, it is one of the key Questions that arise when speaking of Slenderman - or truly any being. With humans, it is a simple answer. We eat external sources of nutrients that our bodies need. The sources can vary depending on personal preferences and tastes. Multi-cellular life has a very basic system. Don't get me wrong, complex on a technical level, but easy to comprehend. You insert something onto one end, sooner or later it the waste comes out filtered to species-specifications from the other. But what of Slenderman?
The currently held theory, though not truly canon, is that he feeds off fear. Without any real basis for this, it came to rise because his contemporary modus operandi is that he stalks those that fear him and know of him. So once could make the assumption that He is fed through the fear he brings, which is why he makes appearances to seemingly only have people fear him. The problem with this is that in the Original Mythos, he didn't make the "poof here I am" appearances to most people. He would gain the trust of children and then abduct them. Similarly, he would mutilate victims and animals without using the "tact" one would associate with current mythos, which if only going based off the original belief structure, would hint that he consumes flesh.
Including the original mythos, there's been no real evidence that fear nourishes him. In the EverymanHYBRID videos, he originally appears due to being imitated and would suggest the stalking and fear being put forth there is retaliatory not for sustenance. Similarly, in MarbleHornets, he shows up in the background even when the characters are in happier situations, thusly showing that the person's fear does not actually nourish him. Though in both examples, there's can be the debate that he was there to observe and interact not to feed.
Another widely held theory, coming from the belief that he is formed through The Tulpa Effect, is that he doesn't feed on fear, in a literal or metaphorical sense, but instead goes with the theory that Slenderman is as strong as the universal belief in Slenderman. This notion would mean that his appearances are to grow his belief-base and therefore his strength. This can be regarded as part of the changes in Slenderman's abilities from the original mythos to contemporary views, as a growth of believers and followers have granted him enough power to not need to work on trust but instead implement his will on individuals.
As with the fear-based feeding pattern, no real evidence exists to support this theory, save for the growth of Slenderman's abilities paralleling his growth in sightings and interactivity. Similarly, a problem with this theory is that he has had cults and follows for centuries, according to the original mythos as well as the Collective, which is a group present at the known earliest since World War II, and who were converted into very powerful beings, far earlier power-wise than the original mythos would tell.
The final theory, and one that was largely held during the original mythos is that he feeds on people directly, via a absorbing life energy or killing them. This theory can be traced back to the mutilation of those that saw Slenderman in the Original Mythos, where animals and humans were mutilated after seeing him. The original mythos had many mutilations and murders attributed to Slenderman, which one could assume to be his feeding method. However, with recent information, that method may in fact stem from the Collective or another organization either underneath Slenderman or opposing him. The absorption part of this theory is found within the roots of the Sickness that plagues those that have prolonged contact with Slenderman. While its been proven to be a type of radiation, notably Sigma Radiation though Jeff commented that radiation may just be the best term for it. Major speculation is that this is a side effect of being stalked by Slenderman though there are few who hold that what the "radiation" is, is actually Slenderman feeding via absoption or that specific radiation marks you as the Slenderman's meal to be torn apart in privacy later. These are all truly just speculation, with positives coming form canon sources, and negatives being that no real proof can be gained from any of this.
In my personal views, the belief theory is the most likely choice, due to the growth comparisons as well as the a high numbers of proxies and suspected proxies, which given the tendril nature of belief, would mean that knowledge of him would spread faster.
Whatever Slenderman uses to nourish himself, if at all, is a mystery. A mystery that may never be solved by those who are not listed on the menu.