Shrimad Bhagavatam just mentions Shri Krishna kicking cart and cart collapsed along with all it's utensils and Villagers Of Gokula rushing to the spot and finds amazed on how cart had collapsed and the kids tell Shri Krishna did the feet and villagers refuse to believe and mentions nothing about Demon Shakatasura. Below is the excerpt from Chapter 7 Dashama Skandha of Shrimad Bhagavatam :
At the time the moon stood in the constellation of Rohinî [after three months] He could turn Himself on His back in His crib. To celebrate this the mothers organized a celebration with a washing ritual. They gathered with music and song and while mother Yas'odâ performed the bathing ceremony hymns were chanted by the brahmins. (5) After Nanda's wife and the other members of the household had finished the bathing, the brahmins, who performed their auspicious mantras, were respectfully honored with food, garments, garlands and cows. Seeing that the child had become sleepy, it was laid aside for the time being. (6) While busily engaged for the utthâna [or 'turning upward'] ceremony she, providing the guests from all over Vraja to their liking, did not hear any of the cries of her child who, wailing to be fed, angrily kicked around its legs. (7) The cart underneath He was put was hit by His delicate feet that were as tender as a new leaf. It turned over so that all the bowls, plates and the sweetness they contained fell to the ground, the wheels and axle got dislocated and the pole was broken [**]. (8) All the men and women of Vraja who being invited by Yas'odâ and Nanda had assembled for the utthâna ceremony witnessed that wondrous event and wondered how the cart out of its own could have been damaged so badly. (9) The children told the dumbfounded gopas and gopîs that it suffered no doubt that, as soon as the child started to cry, it with one leg had dashed it apart. (10) They, unaware of the inconceivable power of that small baby, could not believe it.
Just like Shrimad Bhagavatam Vishnu Purana too goes with same account and does not mention about Sakathasura. Below is the excerpt from Vishnu Purana Chapter 6 Book 5:
ON one occasion, whilst Madhusúdana was asleep underneath the waggon, he cried for the breast, and kicking up his feet he overturned the vehicle, and all the pots and pans were upset and broken. The cowherds and their wives, hearing the noise, came exclaiming, "Ah! ah!" and there they found the child sleeping on his back. "Who could have upset the waggon?" said the cowherds. "This child," replied some boys, who witnessed the circumstance; "we saw him," said they, "crying, and kicking the waggon with his feet, and so it was overturned: no one else had any thing to do with it." The cowherds were exceedingly astonished at this account; and Nanda, not knowing what to think, took up the boy; whilst Yaśodá offered worship to the broken pieces of pots and to the waggon, with curds, flowers, fruit, and unbruised grain.
However Harivamsha supplement to Mahabharata and Mahabharata Tatparya Nirnaya one of the oldest commentary in the Mahabharata by Sri Madvacharya mentions about Demon Sakata. below is the excerpt from Mahabharata Tatparya Nirnaya Chapter 12 :
yadA.a.apa devaH chaturaH sa mAsA.n tatt upanishhkrAmaNam asya chA.asIt |
janmarxam asmin dina eva chA asIt prAtaH kiJNchit tatra mahotsavo.abhavat || 12.89||
kR^iShNa is now four months old and a function called niShkramaNa is due. niShkramaNa means going out. Infant’s first outing from the house. Infant will be taken to his maternal uncle’s house, or to some temple etc as first outing. Till then he is unmoved from house for security reasons. On that day his birth star rohiNi is there marginally. And a great festivity is hosted on that day. [12-89]
tadA shayAnaH shakaTasya so.adhaH padA.axipat taM ditijaM nihantum |
anaH samAvishya diteH suto.asau sthitaH pratIpAya hareH supApaH || 12.90||
On that day kR^iShNa slept under a cart, and kicked that cart in order to eliminate a demon who is his antagonist, and who who entered into the structure of cart. [12-90]
xipto.anasisthaH shakaTAxanAmA sa vishhNunetvA sahitaH papAta |
mamAra chA.ashu pratibhagnagAtro vyatyastachakrAxamabhUdanashcha || 12.91||
Getting the impact from the kick of kR^iShNa, a demon named shakaTa-aksha fell dead together with the cart, and splinterd are his body parts together with the parts of that cart. [12-91]
So Demon Sakata might have entered form of cart and Shri Krishna kicked it, all three main scriptures about Shri Krishna called Bhagavata, Vishnu Purana and Harivamsha emphasise this event about this Lila (Sport) of Shri Krishna, Bhagavatam and Vishnu Purana does not mention about demon , Harivamsha does. Mahabharata Tatparya Nirnaya was written by Shri Madvacharya. In Mahabharata Tatparya Nirnaya instead of viewing Mahabharata as a story work, Madhvacharya clearly gives it the status of Nirnayaka grantha. Sri Madhva also includes Ramayana in this work to show that Mahabharata is a complete work by the divine Sri Veda Vyasa. This work is an excellent exposition of the Mahabharata. It explains some finer aspects of the Mahabharata by supplementing it from other classical works such as Harivamsa, Vishnu Purana, Bhagavatha and others. Bheemasena is the clear hero of the Pandavas, in each and every incident this is underlined by giving lots of proof for each statement. Below is the excerpt of Foreword from Chapter 1 of Mahabharata Tatparya Nirnaya :
So Yes Shri Krishna killed Sakatasura even though Bhagavatam and Vishnu Purana might not have mentioned Demon's name but the main event of Shri Krishna kicking the cart is mentioned.