By RAW, no, due to total cover.
As per this answer,
In a podcast, [Jeremy Crawford] confirmed that you can't target creatures with spells beyond transparent obstacles because spells require a connection between caster and target.
Because the target has total cover, then they cannot be targeted. Crawford also tweets this regarding conjuring animals across an invisible Wall of Force. Conjuring spells require no attack roll, and no saving throw. They specify "a spot that you can see", but Jeremy confirmed that this means you need both uninterrupted line of effect, and to see where you are casting! The Gelatinous Cube does offer total cover, thus negating Telekinesis.
Creatures inside the cube can be seen but have total cover (MM p.242)
This also falls within the general Spellcasting rules.
To target something, you must have a clear path to it, so it can’t be behind total cover.
Spellcasting rules don't actually require sight, because you can target invisible enemies or enemies that you cannot see, according to rules of combat.
When you attack a target that you can’t see, you have disadvantage on the attack roll.
So spells need to specifiy when sight is required.
Regarding the specific beats general rule, it's about direct contradictions. Remember that the spells say "a target that you can see", and not "a target that you only need to see". They are essentially re-enforcing the targeting conditions already existing on spellcasting rules, meaning that targets need to be visible and that there must be an uninterrupted line between them and the caster. Otherwise you could cast spells at invisible targets within range, and roll Attack Rolls with only disadvantage if you could guess their location properly. An exception would be Sacred Flame, that explicitly contradicts the cover rule:
Flame-like radiance descends on a creature that you can see within range. The target gains no benefit from cover for this saving throw.
Keep in mind that certain spells have specific ranges in order to be able to target things that are not visible, or under cover. Dream has Special range, Telepathy has Unlimited range, Locate Object and Misty Step have Self range. Telekinesis, on the other hand, has 60ft range, and Conjure Fey has a range of 90ft.
That being said, the Rule of Cool would be a great application here. Possibly adding a casting check against the Cube's Strength DC (as if someone was physically trying to pull the player out). But this falls under homebrewed rules and DM judgement.