Why do lions sometimes eat their cubs?

 For one, it's important to note there's a huge difference between killing one's own cubs & eating them.

Above: female carries her deceased cub, killed by a male. It wouldn't be unusual for her to consume this cub.

It's not uncommon for cats of all kinds to find their cub deceased and then consume it. There's any number of reasons for why this occurs:

Grief

To ensure no other animal can eat the remains.

To eliminate its scent in the area.

Distress reaction.

Above: this lioness lost her cub to a crocodile, consumed the rest. It's a distress reaction.

There are instances where a lioness will ‘technically' kill their cub and eat it as well. This is usually reserved for instances where the cub is injured, sick, or just died. There's a pretty viral video of a lioness doing this, but you can actually note the time of death of the cub on the video. Prior to that, she's seen trying to revive it.

Other times, mothers will cannibalize a new litter immediately following birth. This happens most frequently in captivity, due to high stress. It also happens in the wild, often in lionesses who got pregnant immediately following a takeover. They either don't trust the new male, it already left, or there's still residual stress from the event.

Other times the mother may be incredibly malnourished, knowing she can’t provide milk for them she eliminates them. It can also occur in first time mothers, for reasons unknown. It's quite rare, though.

We all know male lions are cub killers, but rarely their own. When they takeover a pride they eliminate all the cubs (typically) so they can start their own family with the lionesses. It’s unusual for them to consume them.

Male lions have been documented to kill their own cubs, but it’s rare. This usually isn’t the males’ intent, but is the outcome of a violent incident. It's even rarer for them to then cannibalize them. As that's not a common behaviour in lions, period.

It's important to note that just because we as humans can't relate to, or fully understand, why an animal would consume its young after death, doesn't suggest they didn't care or aren't great mothers. Much of animal behaviour isn't relatable, and therefore shouldn't be judged.

Anyone whose observed big cat mothers in the wild for any amount of time knows just how loving and caring of providers they are--& how incredibly distressed they become when/if separated.