Krishna and Balarama learned from Saandeepani is described in Srimad Bhagavatam (10.45):
SB 10.45.32 — Sāndīpani thought very highly of these two self-controlled disciples, whom he had obtained so fortuitously. By serving him as devotedly as one would serve the Supreme Lord Himself, They showed others an irreproachable example of how to worship the spiritual master.
SB 10.45.33 — That best of brāhmaṇas, the spiritual master Sāndīpani, was satisfied with Their submissive behavior, and thus he taught Them the entire Vedas, together with their six corollaries and the Upaniṣads.
SB 10.45.34 — He also taught Them the Dhanur-veda, with its most confidential secrets; the standard books of law; the methods of logical reasoning and philosophical debate; and the sixfold science of politics.
SB 10.45.35-36 — O King, those best of persons, Kṛṣṇa and Balarāma, being Themselves the original promulgators of all varieties of knowledge, could immediately assimilate each and every subject after hearing it explained just once. Thus with fixed concentration They learned the sixty-four arts and skills in as many days and nights. Thereafter, O King, They satisfied Their spiritual master by offering him guru-dakṣiṇā.
From the PURPORT of SB 10.45.35-36:
The Lords learned (1) gītam, singing; (2) vādyam, playing on musical instruments; (3) nṛtyam, dancing; (4) nāṭyam, drama; (5) ālekhyam, painting; (6) viśeṣaka-cchedyam, painting the face and body with colored unguents and cosmetics; (7) taṇḍula-kusuma-bali-vikārāḥ, preparing auspicious designs on the floor with rice and flowers; (8) puṣpāstaraṇam, making a bed of flowers; (9) daśana-vasanāṅga-rāgāḥ, coloring one’s teeth, clothes and limbs; (10) maṇi-bhūmikā-karma, inlaying a floor with jewels; (11) śayyā-racanam, covering a bed; (12) udaka-vādyam, ringing waterpots; (13) udaka-ghātaḥ, splashing with water; (14) citra-yogāḥ, mixing colors; (15) mālya-grathana-vikalpāḥ, preparing wreaths; (16) śekharāpīḍa-yojanam, setting a helmet on the head; (17) nepathya-yogāḥ, putting on apparel in a dressing room; (18) karṇa-patra-bhaṅgāḥ, decorating the earlobe; (19) sugandha-yuktiḥ, applying aromatics; (20) bhūṣaṇa-yojanam, decorating with jewelry; (21) aindrajālam, jugglery; (22) kaucumāra-yogaḥ, the art of disguise; (23) hasta-lāghavam, sleight of hand; (24) citra-śākāpūpa-bhakṣya-vikāra-kriyaḥ, preparing varieties of salad, bread, cake and other delicious food; (25) pānaka-rasa-rāgāsava-yojanam, preparing palatable drinks and tinging draughts with red color; (26) sūcī-vāya-karma, needlework and weaving; (27) sūtra-krīḍā, making puppets dance by manipulating thin threads; (28) vīṇā-ḍamarukavādyāni, playing on a lute and a small x-shaped drum; (29) prahelikā, making and solving riddles; (29a) pratimālā, capping verses, or reciting poems verse for verse as a trial of memory or skill; (30) durvacaka-yogāḥ, uttering statements difficult for others to answer; (31) pustaka-vācanam, reciting books; and (32) nāṭikākhyāyikā-darśanam, enacting short plays and writing anecdotes.
Kṛṣṇa and Balarāma also learned (33) kāvya-samasyā-pūraṇam, solving enigmatic verses; (34) paṭṭikā-vetra-bāṇa-vikalpāḥ, making a bow from a strip of cloth and a stick; (35) tarku-karma, spinning with a spindle; (36) takṣaṇam, carpentry; (37) vāstu-vidyā, architecture; (38) raupya-ratna-parīkṣā, testing silver and jewels; (39) dhātu-vādaḥ, metallurgy; (40) maṇi-rāga-jñānam, tinging jewels with various colors; (41) ākara-jñānam, mineralogy; (42) vṛkṣāyur-veda-yogāḥ, herbal medicine; (43) meṣa-kukkuṭa-lāvaka-yuddha-vidhiḥ, the art of training and engaging rams, cocks and quails in fighting; (44) śuka-śārikā-pralāpanam, knowledge of how to train male and female parrots to speak and to answer the questions of human beings; (45) utsādanam, healing a person with ointments; (46) keśa-mārjana-kauśalam, hairdressing; (47) akṣara-muṣṭikā-kathanam, telling what is written in a book without seeing it, and telling what is hidden in another’s fist; (48) mlecchita-kutarka-vikalpāḥ, fabricating barbarous or foreign sophistry; (49) deśa-bhāṣā-jñānam, knowledge of provincial dialects; (50) puṣpa-śakaṭikā-nirmiti-jñānam, knowledge of how to build toy carts with flowers; (51) yantra-mātṛkā, composing magic squares, arrangements of numbers adding up to the same total in all directions; (52) dhāraṇa-mātṛkā, the use of amulets; (53) saṁvācyam, conversation; (54) mānasī-kāvya-kriyā, composing verses mentally; (55) kriyā-vikalpāḥ, designing a literary work or a medical remedy; (56) chalitaka-yogāḥ, building shrines; (57) abhidhāna-koṣa-cchando-jñānam, lexicography and the knowledge of poetic meters; (58) vastra-gopanam, disguising one kind of cloth to look like another; (59) dyūta-viśeṣam, knowledge of various forms of gambling; (so) ākarṣa-krīḍa, playing dice; (61) bālaka-krīḍanakam, playing with children’s toys; (62) vaināyikī vidyā, enforcing discipline by mystic power; (63) vaijayikī vidyā, gaining victory; and (64) vaitālikī vidyā, awakening one’s master with music at dawn.
You can also find name of these 64 Kalas at footnote at Gita Press Gorakhpur Edition; at Bhagavatam.org.
Other list/name of 64 Kalas can be found in Devi Bhagavatam (12.11):
Quoting English translation of 12.11 from sacred-texts.com:
O King! Now hear the names of the sixty four Kalâs. They are :-- Pingalâksî, Vis’âlâksî, Samriddhi, Vriddhi, S’raddhâ, Svâhâ, Svadhâ, Mâyâ, Sañgñâ, Vasundharâ, Trîlokadhâtrî, Sâvitrî, Gâyatrî, Tridas’es’vsrî, Surûpâ, Bahurûpâ, Skandamâtâ, Achyutapriyâ, Vimalâ, Amalâ, Arunî, Ârunî, Prakriti, Vikriti, S’rîsti, Sthiti, Samrhiti, Sandhyâ, Mâtâ, Satî, Hamsî, Mardikâ, Vajrikâ, Parâ, Devamâtâ, Bhagavatî, Devakî, Kamalâsanâ, Trimukhî, Saptamukhî, Surâsura vimardinî, Lambosthî, Ûrdhakes’î, Bahusîrsâ, Vrikodarî Ratharekhâhvayâ, S’as’irekâ, Gaganavegâ, Pavanavegâ, Bhuvanapâlâ, Madanâturâ, Anangâ, Anangamathanâ, Anangamekhalâ, Anangakusumâ, Visvarûpâ, Surâdikâ, Ksayamkarî, Aksyobhyâ, Satyavâdinî, Bahurûpâ, S’uchivratâ, Udârâ and Vâgis’î. These are the sixty four Kalâs.
Also visit 18 Vidyas.