Salam wa alaykum. After some investigation, I found the following non-Muslim sources which agree that birthdays are pagan related in their origin:
"The tradition of birthday parties started in Europe a long time ago. It was feared that evil spirits were particularly attracted to people on their birthdays. To protect them from harm, friends and family would come to be with the birthday person and bring good thoughts and wished. Giving gifts brought even more good cheer to ward off the evil spirit. This is how birthday parties began." (Sarno, Et Al - Reading Wonders 5' 2006 Ed. - Rex Bookstore, Inc - Pg. 237).
"The reasons why we have birthday parties goes back to when people believed that good and evil spirits appeared when a child was born and influenced that child for life. These people also believed that it was dangerous for a person to have a change in his or her life. This led people to believe that birthdays were filled with danger since each year marked a change in a person's life." (Ibid - Pg. 238).
"Once upon a time only kings and queens had birthday parties, but, with the advent of the calendar, parties became commonplace. Early birthday parties were raucous affairs intended to drive away evil spirits." (Happy Birthday to You! - Ariel Books - Pg. 54).
"The birth of the birthday cake dates back to the ancient Greeks. It was their custom to present round honey cakes to Artemis, their goddess of the moon - and childbirth." (Ibid - Pg. 59).
"It is said that the earliest birthday parties were conducted because of belief that evil spirits visit on one's birthday. The gathering of friends and family, along with the lighting of candles, represent methods of protection from the threat posed by these evil forced." (Linda S. Watts - Encyclopedia Of American Folklore - Infobase Publishing, 2007 - Pg.40).
"The tradition of birthday parties began in Europe. People feared evil spirits were attracted to people on their birthdays. For protection, their friends and family would come over, bringing good wishes and presents to ward off the evil spirits." (Lisa Thompson - Cordially Invited: Have You Got What It Takes to Be an Event Planner? - Compass Point Books, 2008 - Pg. 14).
"The reason we have a cake with candles is also not known for sure. Some people think it's because a long time ago, in Greece, people used to make a round (or moon-shaped) cake for the goddess of the moon, and light candles and torches to send her messages, wishes or prayers. This might be how we started the tradition of having cakes and blowing out the candles to make a wish." (R.I.C. Publications - Comprehending Our World - R.I.C. Publications, 2008 - Pg. 49).
"The obvious question is this: what is the origin of birthdays? Birthdays were originated through astrology. We need to understand that YHWH's Scriptural calendar was replaced with the Roman calendar, which had 12 months and 385 days. The months were given pagan names/titles and this calendar made it very each for a person to keep track of his birthday, because he could look to the stars and horoscopes, instead, of YHWH. Whereas, YHWH's Scriptural calendar would mean a person's birthday would be very hard to fund each year. Maybe this fact, in and of itself, is revealing to us that YHWH doesn't what us to observe birthdays!
Modern birthday celebrations find their roots in Germany, where gifts were given and candles were lit. The lit candle have honor to the Greek moon goddess, Artemis. Wishing a person "Happy Birthday" and using noisemakers were to scare off evil spirit." (Diane L. Otto - Guess What I Discovered On The Way To Church? - Xulon Press, 2007 - Pg. 402).
"The tradition of birthday parties began centuries ago in Europe as a deterrent to evil spirits, believed to be attracted to people on their birthdays. To protect the person having the birthday, friends and family would drop by, bringing good thoughts and wishes. Giving gifts was thought to be an even more effective strategy to ward off evil spirits." (Deborah Kesten & Dean Ornish - The Healing Secrets of Food: A Practical Guide for Nourishing Body, Mind, and Soul - New World Library, 2001 - Pg. 46).
"An ancient Greek custom of honoring Artemis' birthday with a Full Moon cake is still seen today in our birthday cakes. The Greeks even put lighted candles on the Moon cake." (Deanna J. Conway - Moon Magick: Myth & Magick, Crafts & Recipes, Rituals & Spells - Llewellyn Worldwide, 1995 - Pg. 74).
"Many people believe the idea of a birthday cake came from ancient Greece. Ancient Greeks made cakes as offerings to the goddess of the moon. These cakes were round like a full moon. Later, candles were added to make the cakes glow like a full moon." (Gina DeAngelis - Greece - Compass Point Books, 2003 - Pg. 19).
"The popular custom of lighting candles on a birthday cake, making a wish, and then blowing out the candles is one that is carried out in many parts of the world. Most people are unaware, however, that this custom is actually remnants of an age-old Pagan ritual. In ancient Greece, Artemis (virgin goddess of the hint, lunar deity, and Greek equivalent to the Roman goddess Diana) was honored each year on the 24th day of May, the date of her birth, according to Greek mythology. In special temples consecrated to her worship, moon-shaped cakes adorned with burning cakes would be places upon the altar as offerings.
After the advent of the Christian faith in Greece, the worship of the ancient gods was banned by law and their temples destroyed or converted to the uses of the New Religion. However, many of the old ways, including the lighting of the candles on birthday cakes, managed to survive into the present day." (Gerina Dunwich - Exploring Spellcraft: How to Create and Cast Effective Spells - Career Press, 2001 - Pg. 97-98).
Also, refer to: (
Zsuzsana Summer - The Now Age: Demystifying Spirituality, the New Age and the Metaphysical - iUniverse, 2004 - Pg.65 - Source: goo.gl/8c40).