Preheat oven to 425ºF (220ºC). Pat turkey dry with paper towel. Rub with half the oil. Season with 2 tsp (10 mL) salt and 1 tsp (5 mL) pepper all over and inside cavity. Tie legs together with kitchen twine and tuck in wing tips. Place turkey, breast-side up, on rack in roasting pan. Roast in lower-third of preheated oven 30 min., then reduce temperature to 325°F (160°C) and continue to cook approx. another 2 hr. In last hr. of cooking, baste once or twice with pan drippings.
Meanwhile, make cranberry glaze. In saucepan, bring cranberry cocktail and maple syrup to a boil. Stir in cranberries and return to a boil. Reduce heat to medium, stirring occasionally, 10 to 12 min., until cranberries soften. To a small bowl, remove 1/4 cup (60 mL) of the cranberries from the sauce; set aside.
Into saucepan mixture, stir 1/4 cup (60 mL) water and use immersion blender to puree until smooth; let cool in saucepan. In last 30 min. of cooking, use 1/4 cup (60 mL) of loosened cranberry glaze to baste turkey, 2 to 3 times.
When turkey registers 185°F (85°C) on instant-read meat thermometer inserted into thickest part of inner thigh, transfer turkey to serving platter. Remove kitchen twine, tent loosely with foil and let rest 30 min.
Increase oven to 425ºF (220ºC). In bowl, toss squash cubes with remaining oil, pumpkin pie spice, remaining salt and pepper. Arrange on parchment paper-lined baking sheet in single layer. Bake 18 to 20 min., or until golden brown and tender.
Add reserved softened cranberries back into remaining cranberry glaze. Slice turkey and serve with roasted squash and cranberry glaze.
If turkey browns too quickly during roasting, tent with foil.