The Valmiki Ramayana mentions about SKandha, when Viswamitra narrates about it to Rama and Lakshmana. By chance do Kamban Ramayana make similiar mention either in the same context or in another context.
I think you are referring to these two verses from Bāla-kāṇḍa of Vālmīki Rāmāyaṇa where Viśvāmitra is narrating the descent of Gaṅgā to Earth.
Although I'm not sure what you mean by "mention of Skanda Purāṇa". Why will Rāmāyaṇa mention or reference a Purāṇa?
स्कंद इति अब्रुवन् देवाः स्कन्नम् गर्भ परिस्रवात् |
कार्तिकेयम् महाबाहुम् काकुत्स्थ ज्वलन उपमम् || १-३७-२७
27. kaakutstha = oh, Rama of Kakutstha; jvalana upamam = flare of fire, similar to - glow; mahaa baahum = ambidextrous; garbha parisravaat skannam = from womb's, secretions, who slid down; such a; kaartikeyam = Kaartikeya - is called; devaaH = gods; skanda iti abruvan = Skanda, thus, they called him - in its lexical meaning - to slid, who glissaded.
And gods called that boy, oh, Rama of Kakutstha, whose glow is like that of flaring fire and who is ambidextrous as 'Skanda' for he slid down from the secretions of a womb. [1-37-27]
प्रादुर्भूतम् ततः क्षीरम् कृत्तिकानाम् अनुत्तमम् |
षण्णाम् षड् आननो भूत्वा जग्राह स्तनजम् पयः || १-३७-२८
Then an unexcelled milk instantly came forth from the breasts of the six Krittika-stars, and becoming a six-faced one that boy too sucked that milk from the six Krittika-stars at the same time. [1-37-28]
You can read the English translation of Kamba Rāmāyaṇa (by P.R. Ramachander) here. I did not find a single reference to 'Skanda' on that website. Although there are couple of references to Lord Subramanya. One such mention is in the conversation between Hanumān (disguised as a brāhmaṇa) and Rāma from Kiṣkindhā-kāṇḍa:
[Hanumān says to Rāma]
3774. Since you are the Lord who has the power of creation,
Of the devas who do not blink their eyes to beings,
Which are fixed as well as moving
And have the capacity of protecting
The three types of seven worlds, it is easy to tell for us that you would protect,
Only us as we who seek protection from you who are like Lord Subramanya,
And is there any other better benefit that would come to us.
The translator is equally amazed at why Kamban has left out the birth story of Kārtikeya from his work. He writes:
Kamba Ramayanam – Bala Kandam – Padalam 8-10
8. Velvi Padalam
The chapter on fire sacrifice
(This chapter tells how sage Viswamithra gave divine arrows to Rama. Viswamithra tells the store of his forefathers and also about his father Gadhi, his sister Kaushiki, the story of Mahabali and Vamana and tells him about Sidhasrama where Lord Vishnu did penance. Then Viswamithra starts the Yaga, after the sixth day the asuras come. Rama kills Subahu and throws out Mareecha in the sea and also kills lot of asuras. The Yaga is satisfactorily completed.
Apart from these aspects the Valmiki Ramyana in detail tells the story of Ganga as well as the birth of Karthikeya. I am not able to tell why Kambar chose to leave out the story of Karthikeya, in spite of Karthikeya (Subrahmanya) being the main God of Tamil Nadu.)
The translator also notes in his introduction that Kamban condensed Vālmīki Rāmāyaṇa to about 12,000 verses:
Without any doubt whatsoever, the story of Rama was popularized by the Ramayana written by Valmiki. This has been translated in to almost all the main languages in India. Kamban (who is supposed to have lived between 1180-1250 AD) one of the greatest poets of Tamil Nadu translated it in to Tamil. He preferred to call it Ramavatharam (the incarnation of Rama). In this great job, he received the support of Thiruvennai nallur Chadayappa vallal, a great philanthropist who lived in Tamil Nadu at that time. Kamban who admired this Vallal mentions his name once in 1000 verses in his book.
Kamban did not do a literal translation of Valmiki Ramayana. He condensed it a lot, while adding some portions of his own. While Valmiki's great epic consists of 24000 verses, Kamaban's translation only contains 12000 verses. Though he adopted the six book (Kandam) concept of Valmiki, he has not adopted the sargam concept of Valmiki. He has divided the Kandas in to Padalams and his Padalams are not direct translation of the Sargams of Valmiki. His book has only 123 Padalams.
Kamban also did not adopt the story of Valmiki verbatim and made changes to the story. There is a folk story that the entire Kamba Ramayanam was written by Lord Ganesa as per his dictation.