Published in 1952 , Isaac Asimov's David Starr, Space Ranger , the first novel of the Lucky Starr series, has aliens that have shed their material bodies and became beings made of pure energy.
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Out of the Silent Planet (1938) has beings without material bodies, although they don't evolve that way.
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The classic 1956 film Forbidden Planet likely gave the energy being thing a good boost when it turned out that the Krell's attempt at peaceful discorporation was disrupted by "Monsters from the Id!"Energy beings, and beings of light have been around for a long time, but it looks like usage of 'being of light', got a big and sustained boost around 1974:
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Whether this answer is acceptable to you will depend on how you define "advanced race," "fantasy," and "beings of light," but here goes...
As most modern stories which talk about "beings of light" tend to do so with some sort of religious or spiritual overtone, it is probably no surprise that the concept would have originated in the realm of religion and spirituality.
Stories of people turning into angels, demons, ghosts, gods, or other spirtual beings have been around for millennia, and in many cases these types of spirit-beings (especially angels and gods) are portrayed as "beings of light".
A few examples I could find, in roughly reverse chronological order: 1843 - A Christmas Carol ~500 AD - Christian artwork begins to show the ressurected Jesus as a "being of light" 61-115 AD - An Ancient Ghost Story by Pliny
the Younger ~500 BC - Greek mythology has the myth of the phoenix , which dies, to be regenerated as the sun ???
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By some accounts ( 1 ) at least some segments of Hindusm hold that god-like or angelic devas may have been humans in past lives 2494 BC -
The Egyptian god Ra was the sun, or represented by the sun, although he was not, to my knowledge, believed to have been a lesser person/being previously 2780 BC -
The Egyptian god Atum , also represented by the sun 3000?
BC - Egyptians believed the deceased Pharoahs would become gods after death and "ascend to the sky and dwell among the stars
" I think this last one is both the oldest I can find, and the closest match to your description, leaving only the question of how you define an "advanced race."
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I think a very important, fitting term that's still missing in this Q&A is Transcendence .
This article discusses that sci-fi trope in detail and names
a bunch of early stories that qualify.
For example, Arthur C. Clarke's "Childhood's End" (1950 orig.), Theodore Sturgeon's "The Cosmic Rape" (1958), Alfred Besters' "Tiger!
Tiger" (1957)
Transcendence can be considered as a wildcard symbol for what comes after human/AI intelligence soars (by definition) beyond the comprehension of pre-singularity minds [...]
humanity departing or evaporating into unknowable realms
However, they also note a difference between the positive transformation of transcendence and becoming immaterial in general: Not every story of escape from the bonds of matter achieves transcendence:
in Isaac Asimov's "Eyes Do More Than See" (April 1965 F&SF), humans who have attained Immortality as energy beings mourn the loss of bodies and bodily sensations.
- See more at: http://www.sf-encyclopedia.com/entry/transcendence#sthash.kYMdCuMx.dpuf
But out of universe, why does this happen in many sci-fi stories?
A tonal shift towards transcendence can be a convenient way to conclude a story whose narrative crescendo can increase no further.
[...] "... you build to a certain climax and there's no way to go to finish it off, except mystic [...]
you gotta go mystic".
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Though not the first because of its 1975 publication, the Illuminatus!
Trilogy by Robert Shea and Robert Anton Wilson features accounts of human beings becoming beings of pure energy through a process called "transcendental illumination", which is usually triggered by the deaths of hundreds or thousands of human beings.
It also draws heavily upon the Cthulhu Mythos, and both is and contains hilarious parodies of Ayn Rand and Atlas Shrugged .
Hail Eris!
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In the Malloreon of David Eddings, Star Trek, and the game Loom, among many others, there are races of beings who are shown as being highly advanced, who have the goal of becoming beings made of pure light (although in Loom, some became light, some became birds, etc,).  When did evolving into beings of light first occur in Scifi or fantasy?
What is the first instance of advanced races becoming beings of light in scifi and fantasy?
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<history-of>
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Beings of light can be found in Arthur C. Clarke's "Childhood's End" (1950 orig.), Theodore Sturgeon's "The Cosmic Rape" (1958), Alfred Besters' "Tiger!", "Trilogy"  by Robert Shea and Robert Anton Wilson, Asimov's "David Starr, Space Ranger", the 1956 film "Forbidden Planet" and "The Illuminatus". Beings first evolved into light in Childhood’s End in 1950, though Tiger by Besters and Trilogy by Shea and Anton Wilson may have been earlier. 
Beings evolving into light occurred in the following: Space Rangers (1952); Forbidden Planet (1956); Childhood’s End (1950); the Cosmic Rape (1958); and the Illuminatus (1975). Tiger by Alfred Besters and Trilogy by Robert Shea and Robert Anton Wilson are also possibilities. 