Hi
When moving forward, the block in front needs to be checked.
When falling block below you is checked.
Just to note, when jumping forward, you can’t jump forward if there is a block there, but as soon as you are higher than the block you would then be able to move forward, then the block below you is the new ground height. So the block doesn’t stop you jumping, only jumping forward. The vertical component of your jump is unaffected by forward motion. As herosgrave mentioned its quadratic - but moving forward has no effect on you upward or downward movement.
Because they are cubes, ordered in a grid, I think just taking the int of your position tells you if you are in a block or not.
The only consideration for collision if you want your character to have a physical size and not be a point is that it has a bounding box, and you could test each corner.
This does created additional problems when moving towards the corner of a block.
AABB may be a good way to go. I may do that later, but there are others ways around that.
You also have to test more than one block if you character is higher than one block, in case you want to go under blocks!