How Ganesha Gets the Fruit of Knowledge from Shiva

Narada once found a rare pommegranate fruit that had the nectar of the Supreme Knowledge hidden in it and gave it to Lord Shiva. His children Ganesha and Kartikeya (Murugan/Subramanya) wanted it for themselves.

Shiva said whoever went round the entire universe and came back first would get the coveted fruit. Kartikeya left at once, riding on the peacock, his super fast vahana. Ganesh was fully aware of the limitations of his own stout body and the speed of the rat, his vahana.

But He was wise. He went round his parents, and bowed to his parents. "I have gone around the world," he said, "and have returned before my brother." To the astounded onlookers, he said, "My parents Shiva and Shakti are the Whole Universe. The Whole Universe is within them".

Muruga returned in an instant, yet Ganesha had completed his round in just a tiny fraction of an instant earlier and won the contest, and carried the fruit as the trophy.

Murugan got angry. How he reaches Palani and takes his residence there is narrated here-> Palani, Kavadi and Idumban

The story illustrates that you can see every object inside the 'Shivam' and you can see 'Shivam' in every object.

The fruit in the above story represents knowledge or 'Jnana'. Knowledge is indivisible: it has to be obtained in its entirety. Muruga went round the Universe and showed it was the manifestation of the Absolute. He is therefore called the 'Jnana Pandita'.

The entire universe functions on the basis of three powers namely Iccha Shakti, Kriya Shakti and Jnana Shakti. Jnana Shakti is the power of the intellect; the Iccha Shakti is the power of mind; and the Kriya Shakti is the power of the senses. The desire to do a task is the work of Ichcha Shakti and it propels the person into action using the knowledge about the task. This knowledge is Jnana Shakti and it powers the Intellect. To actually do the work, a person needs the cooperation of the sense organs. When the Jnana Shakti connected to the Absolute Power, the person can use the Ichcha Shakti and Kriya Shakti to perform the action with perfection.

More specifically, a devotee has to acquire the desire and the right action to know the Brahman. If Murugan is the representation of Brahman, then Devasena and Valli are the modes which a sadhak has to acquire to be a knower of that Brahman.

Here's some songs that say Ganesha got the fruit for going around His father :
umbartharu
தந்தை வலத்தால் அருள்கை கனியோனே

The song sivagyana pundarika mentions that Parvati Devi gave the pommegranate fruit to the bright elephant God Ganesha.
ஒளிரானை யின்கரமில் மகிழ்மாது ளங்கனியை
யொருநாள்ப கிர்ந்தவுமை யருள்பாலா

That Murugan was angry with His father and went to Pazhani is mentioned in the song pudavaikkaNi thugil.

படியிற் பெருமித தகவுயர் செம்பொற்
கிரியைத் தனிவலம் வரஅர னந்தப்
பலனைக் கரிமுகன் வசமரு ளும்பொற் பதனாலே
பரன்வெட் கிடவுள மிகவும்வெ குண்டக்
கனியைத் தரவிலை யெனஅருள் செந்திற்
பழநிச் சிவகிரி தனிலுறை கந்தப் பெருமாளே.

The song enakku chattru sings about it thus:
கனிக்குத் திக்கு அனைத்துச் சுற்றிட பச்சைக் கனப் பக்ஷிக்கு
இடைப் புக்குக் களிப்புக்குத் திரிவோனே

The song kadalai payarodu praises the speed and elegance of Murugan's ride through the universe on His peacock:

நிகரி லயில்வெயி லெழுபசு மையநிற முளதான
நடன மிடுபரி துரகத மயிலது
முடுகி கடுமையி லுலகதை வலம்வரு
நளின பத...

and also in kadalai pori

வட வரையின் முகடு அதிர
ஒரு நொடியில் வலம் வரு மரகத மயில் வீரா

The song எழுதிகழ் புவன describes the beauty of this super-fast circumambulation.
எழுதிகழ் புவன நொடியள வதனி
லியல்பெற மயிலில் வருவோனே

Thiruvelaikkaran vaguppu desribes the incidents thus:
ஆரமது ரித்தகனி காரணமு தற்றமைய
னாருடனு ணக்கைபரி தீமைக் காரனும்
ஆகமம்வி ளைத்தகில லோகமு நொடிப்பளவில்
ஆசையொடு சுற்றுமதி வேகக் காரனும்