Converting a 10″ Bundt recipe to an 8″ square pan
Batter scales with volume, not with width. A 10″ Bundt pan holds about 12 cups filled to the brim, and an 8″ square pan holds 8 cups, so you need 33% less batter. Multiply every ingredient — including the eggs, which is the awkward one — by ⅔×.
The number people miss is depth. Two pans can hold the same volume and still bake completely differently, because what matters is how thick the batter sits: volume divided by bake surface. Here that moves from about 1.6″ to 1.2″. Batter sits shallower in the new pan. Check 10–15% earlier than the recipe states (an estimate) — shallower batter bakes faster. (Bundt and tube depths are approximate: their ring-shaped bake area isn't published, so we estimate it.)
Coming out of a Bundt is easier than going in. A Bundt's central column lets heat through the middle of the batter, so a plain round pan of the same capacity bakes more slowly at the centre. Give it a little longer and test in the thickest part.
How many pans one batch fills
A 10″ Bundt recipe comes to about 1½ 8″ square pans, which doesn't divide neatly. Three honest options: fill two pans and accept that the last comes out shallower; scale the recipe by ⅔× for a single pan; or scale it by 1⅓× to fill both properly. Batter left standing while an earlier pan bakes loses its lift, so get them all in the oven together where you can.
A caution worth reading
Volume conversions hold well for cakes, brownies and quick breads — anything poured. They hold less well for recipes where structure comes from the pan itself: a delicate chiffon or angel food climbs the ungreased side of a tube pan, and a loaf's shape is part of how it bakes. For those, scale the ingredients by all means, but expect the texture to shift, and use the skewer rather than the recipe's clock.